Determine the units for output and input values. The rate, t. x We use algebra to find slope-intercept form of the linear equation. The point-slope form of a linear equation takes the form. Here's a link to a screenshot of an example: http://imgur.com/UC1j1su 0,1 To write the rule of a function from the table is somehow tricky but can be made easier by . A linear function is a function whose graph is a line. We can move from one form to another using basic algebra. form ax plus by is equal to c, where these are just two A line with a slope of zero is horizontal as in Figure 5(c). Given a word problem that includes two pairs of input and output values, use the linear function to solve a problem. (4,10), Passes through N, To graph, you must plug in 0 for either x or y to get the y- or x-intercept. We know that ). The function is increasing because D(t) ), Find the equation of the line that passes through the following points: (2a,b)(2a,b) and If ff is a linear function, f(0.1)=11.5,andf(0.4)=5.9,f(0.1)=11.5,andf(0.4)=5.9, find an equation for the function. Solving a Linear Function - Algebra-Class.com , Find the change of population per year if we assume the change was constant from 2008 to 2012. 2 www.cbsnews.com/8301-501465_1ay-study-says/. 1 So let's do slope intercept And now to get it in slope Therefore, the same line can be described in slope-intercept form as \(y=\dfrac{1}{2}x+7\). Our finishing x-coordinate The slope determines if the function is an increasing linear function, a decreasing linear function, or a constant function. Therefore, Ilyas weekly income, I,depends on the number of new policies, \(n\), he sells during the week. The population of a city increased from 23,400 to 27,800 between 2008 and 2012. From the table, we can see that the distance changes by 83 meters for every 1 second increase in time. the slope of the line, then putting that line in point , \[\begin{align*} y1&=2(x4) \\ y1&=2x8 &\text{Distribute the 2.} [latex]\begin{array}{llll} y - 1=2\left(x - 4\right)\hfill & \hfill \\ y - 1=2x - 8\hfill & \text{Distribute the }2.\hfill \\ \text{}y=2x - 7\hfill & \text{Add 1 to each side}.\hfill \end{array}[/latex]. It w, Posted 11 years ago. Interpret the slope as the change in output values per unit of the input value. We can use these points to calculate the slope. 1 \\ y&=-\dfrac{1}{2}x+7 &\text{Add 4 to each side.}\end{align*}\]. we can manipulate it to get any of the other ones. We can interpret this as Ilyas base salary for the week, which does not depend upon the number of policies sold. Otherwise, the process is the same. Sonya is currently 10 miles from home and is walking farther away at 2 miles per hour. 1 Consider the graph of the line \(f(x)=2x+1\). ) Therefore we know that m=15.m=15. Analyzing the slope within the context of a problem indicates whether a linear function is increasing, decreasing, or constant. Because we are told that the population increased, we would expect the slope to be positive. add 6 to both sides of this equation. minus negative 3, so it'll end up becoming x plus 3. y So the population increased by 1,100 people per year. (0,3), x intercept at (5,0)(5,0) and y intercept at (0,4)(0,4). If [latex]f\left(x\right)[/latex]is a linear function, and [latex]\left(2,3\right)[/latex]and [latex]\left(0,4\right)[/latex]are points on the line, find the slope. Restate this function in words. We could also write the slope as \(m=0.6\). (4,3). For example, suppose we are given an equation in point-slope form, So the slope must be: m= rise run = 4 2 = 2 m = rise run = 4 2 = 2. Write the equation of a line parallel or perpendicular to a given line. Direct link to Ansh's post I'm not sure, but the way, Posted 10 years ago. There are several ways to represent a linear function, including word form, function notation, tabular form, and graphical form. 2 =4 Example \(\PageIndex{1}\): Using a Linear Function to Find the Pressure on a Diver, Example \(\PageIndex{2}\): Deciding whether a Function Is Increasing, Decreasing, or Constant, Example \(\PageIndex{3}\): Finding the Slope of a Linear Function, Example \(\PageIndex{4}\): Finding the Population Change from a Linear Function, Example \(\PageIndex{5}\): Writing Linear Equations Using a Point and the Slope, Example \(\PageIndex{6}\): Writing Linear Equations Using Two Points, Example \(\PageIndex{7}\): Writing an Equation for a Linear Function, Example \(\PageIndex{8}\): Writing an Equation for a Linear Cost Function, Example \(\PageIndex{9}\): Writing an Equation for a Linear Function Given Two Points, Example \(\PageIndex{10}\): Using a Linear Function to Determine the number of Songs in a Music Collection, Example \(\PageIndex{11}\): Using a Linear Function to Calculate Salary Plus Commission, Example \(\PageIndex{12}\): Using Tabular Form to Write an, Representing a Linear Function in Word Form, Representing a Linear Function in Function Notation, Representing a Linear Function in Tabular Form, Representing a Linear Function in Graphical Form, Determining whether a Linear Function Is Increasing, Decreasing, or Constant, Writing the Point-Slope Form of a Linear Equation, Writing the Equation of a Line Using a Point and the Slope, Writing the Equation of a Line Using Two Points, Writing and Interpreting an Equation for a Linear Function, Modeling Real-World Problems with Linear Functions, Example \(\PageIndex{12}\): Using Tabular Form to Write an Equation for a LinearFunction, source@https://openstax.org/details/books/precalculus. a function with a negative slope: If \(f(x)=mx+b\), then \(m<0\). To find the linear equation you need to know the slope and the y-intercept of the line. is calculated. x ( To restate the function in words, we need to describe each part of the equation. See Figure \(\PageIndex{7}\). ) 2 We can interpret this as Ilyas base salary for the week, which does not depend upon the number of policies sold. Point-slope form of a linear equation takes the form. 6 is negative 6. You wouldnt have to. x x We can convert it to the slope-intercept form as shown. Determine whether a linear function is increasing, decreasing, or constant. we get rid of it on the left-hand side, so let's as follows, where y y is the vertical displacement and x x is the horizontal displacement. [latex]\begin{array}{l}y-{y}_{1}=m\left(x-{x}_{1}\right)\\ y - 1=\frac{1}{3}\left(x - 0\right)\end{array}[/latex]. 8,1 So you would get 8x -2*0 =24 or 8x =24. We can see from the graph in Figure 3 that the y-intercept in the train example we just saw is All we have to do is we say y So this is a particular The cost Ben incurs is the sum of these two costs, represented by \(C(x)=1250+37.5x\). Write the point-slope form of an equation of a line with a slope of 3 that passes through the point x Linear functions can be written in the slope-intercept form of a line. b Be careful using the proper notation for functions when displaying your a. Linear equations are fundamental to algebra, and thus fundamental to all higher mathematics. If Site: http://mathispower4u.com The letter x x represents the independent variable and the letter y y represents the dependent variable. Let use \((0,1)\) for our point. The relationship between the distance from the station and the time is represented in Figure \(\PageIndex{2}\). A teen has an unlimited number of texts in his or her data plan for a cost of $50 per month. and and and The slope is 3, so m=3.m=3. equal to mx plus b, where once again m is the slope, b is the Both equations describe the line shown in Figure \(\PageIndex{8}\). Calculate the change of output values and change of input values. Write the point-slope form of an equation of a line with a slope of For the following exercises, which of the tables could represent a linear function? If we wanted to then rewrite the equation in slope-intercept form, we apply algebraic techniques. y= Writing a Linear Function | College Algebra Corequisite - Lumen Learning 3, right there. 4.2: Modeling with Linear Functions - Mathematics LibreTexts 1 Now we can substitute these values into the general point-slope equation. Direct link to C Ethan Smith's post I think y=mx+b is the eas, Posted a month ago. Up until now, we have been using the slope-intercept form of a linear equation to describe linear functions. and The speed is the rate of change. minus our x-coordinate is negative 3, x minus negative \[\begin{align*} y-1&=2(x-5) \\ y-1&=2x-10 \\ y&=2x-9 \end{align*}\]. negative 2/3, so you get y minus 6 is equal to-- I'm just 0,7 We can use the function relationship from above, Graph linear functions. Use the points to calculate the slope. Then we use algebra to find the slope-intercept form. We know that [latex]m=2[/latex]and that [latex]{x}_{1}=4[/latex]and [latex]{y}_{1}=1[/latex]. Next, we substitute the slope and the coordinates for one of the points into the general point-slope equation. Then rewrite it in the slope-intercept form. Another way to represent linear functions is visually, using a graph. is a linear function, and and When she plants 34 stalks, each plant produces 28 oz of beans. Expert Maths Tutoring in the UK - Boost Your Scores with Cuemath to do is get it into the standard form. 0,4 Think of the units as the change of output value for each unit of change in input value. What is cost per session? are not subject to the Creative Commons license and may not be reproduced without the prior and express written Let me make this very clear, I Direct link to CubanMissileCrisis's post At 7:25,Sal says that the, Posted 10 years ago. In the real world, problems are not always explicitly stated in terms of a function or represented with a graph. We can write the given points using coordinates. D(t)=83t+250, 2 Accessibility StatementFor more information contact us atinfo@libretexts.org. Find and interpret the rate of change and initial value. x From the table, we can see that the distance changes by 83 meters for every 1 second increase in time. 4,1 3,2 4,1 With this formula, we can then predict how many songs Marcus will have in 1 year (12 months). 3,2 For the following exercises, find the slope of the lines graphed. Writing exponential functions from graphs - Khan Academy The value of bb is the starting value for the function and represents Ilyas income when n=0,n=0, or when no new policies are sold. (4,11) His production costs are $37.50 per item. Graph the function ff on a domain of [ 10,10 ]:fx)=2,500x+4,000[ 10,10 ]:fx)=2,500x+4,000. (0,250) We can write the formula N(t)=15t+200.N(t)=15t+200. This is also known as the "slope.". x Identify two points on the line, such as \((0, 2)\) and \((2,4)\). Write an equation for a linear function given a graph of any interpretation directly on the graph. x If we wanted to find the slope-intercept form without first writing the point-slope form, we could have recognized that the line crosses the y-axis when the output value is 7. (0,3) Each year in the decade of the 1990s, average annual income increased by $1,054. and y ) Substitute the y- intercept and slope into slope-intercept form of a line. 5= (5 2)+b =10+b 5 = (52)+b = 10 +b. These are the same equations, Example 1. We can use the coordinates of the two points to find the slope. N, However, we often need to calculate the slope given input and output values. \(f(x)=mx+b\) is a constant function if \(m=0\). multiply both sides of this equation by 3. Now what is the change in y? Use the two points to calculate the slope. Given two values for the input, \(x_1\) and \(x_2\), and two corresponding values for the output, \(y_1\) and \(y_2\)which can be represented by a set of points, \((x_1,y_1)\) and \((x_2,y_2)\)we can calculate the slope \(m\), as follows, \[\begin{align*} m &= \dfrac{\text{change in output (rise)}}{ \text{change in input (run)}} \\[4pt] &= \dfrac{{\Delta}y}{ {\Delta}x} = \dfrac{y_2y_1}{x_2x_1} \end{align*}\], where \({\Delta}y\) is the vertical displacement and \({\Delta}x\) is the horizontal displacement. ( Determine whether a linear function is increasing, decreasing, or constant. This page titled 2.1: Linear Functions is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. One example of function notation is an equation written in the form known as the slope-intercept form of a line, where ( Recall that the slope measures steepness. ). 4 b are licensed under a, Introduction to Polynomial and Rational Functions, Introduction to Exponential and Logarithmic Functions, Graphs of the Other Trigonometric Functions, Introduction to Trigonometric Identities and Equations, Solving Trigonometric Equations with Identities, Double-Angle, Half-Angle, and Reduction Formulas, Sum-to-Product and Product-to-Sum Formulas, Introduction to Further Applications of Trigonometry, Introduction to Systems of Equations and Inequalities, Systems of Linear Equations: Two Variables, Systems of Linear Equations: Three Variables, Systems of Nonlinear Equations and Inequalities: Two Variables, Solving Systems with Gaussian Elimination, Sequences, Probability and Counting Theory, Introduction to Sequences, Probability and Counting Theory, Finding Limits: Numerical and Graphical Approaches, Shanghai MagLev Train (credit: kanegen/Flickr), The slope of a function is calculated by the change in, http://www.chinahighlights.com/shanghai/transportation/maglev-train.htm, https://openstax.org/books/precalculus-2e/pages/1-introduction-to-functions, https://openstax.org/books/precalculus-2e/pages/2-1-linear-functions, Creative Commons Attribution 4.0 International License. Fill in the missing values of the table. =1. This relationship may be modeled by the equation, \(P(d)=0.434d+14.696\). The fixed cost is present every month, $1,250. Compute the rate of growth of the population and make a statement about the population rate of change in people per year. x m>0. And the way to think about OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. I think y=mx+b is the easiest formula. Write the equation of a linear function given its graph. A linear function may be increasing, decreasing, or constant. The value of \(b\) is the starting value for the function and represents Ilyas income when \(n=0\), or when no new policies are sold. The population of a small town increased from 1,442 to 1,868 between 2009 and 2012. Now we can substitute the slope and the coordinates of one of the points into the point-slope form. When using standard form, a a, b b, and c c are all replaced with real numbers. ( f(1)=4 3.3: Domain and Range - Mathematics LibreTexts f(5)=1 Access this online resource for additional instruction and practice with linear functions. P, Fortunately, we can analyze the problem by first representing it as a linear function and then interpreting the components of the function. ( Or when y changed by negative 1, x changed by 4. to draw a graph, represented in Figure 3. Determine the initial value and the rate of change (slope). And when someone puts this x (0,0). x, and a particular y. 1 3 Given a linear function f and the initial value and rate of change, evaluate f ( c ). ( m Questions Tips & Thanks the same equation. \[\begin{align*} yy_1&=m(xx_1) \\ y1&=2(x4) \end{align*}\]. There are several ways to represent a linear function, including word form, function notation, tabular form, and graphical form. Find the change of population per year if we assume the change was constant from 2009 to 2012. f(x) where 1 \[\begin{align*} y-y_1&=m(x-x_1) \\ y-1&=\dfrac{1}{3}(x-0) \end{align*}\]. The costs that can vary include the cost to produce each item, which is $37.50 for Ben. We went from negative 3 to To find the rate of change, divide the change in the number of people by the number of years. \[\begin{align*} m&=\dfrac{y_2-y_1}{x_2-x_1} \\ &=\dfrac{4-2}{-2-0} \\ &=\dfrac{-6}{-2} \\ &=3 \end{align*}\]. The domain is comprised of all real numbers because any number may be doubled, and then have one added to the product. Write an equation for a linear function given a graph of \(f\) shown in Figure \(\PageIndex{11}\). In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points. Yes. ( The slope-intercept equation of the line is Substitute the values into \(f(x)=mx+b\). Find the change of population per year if we assume the change was constant from 2008 to 2012. ) Some courses share the same topics so they just put the same videos. x The slope is 3, so \(m=3\). We have a point, we could pick Determine the units for output and input values. that, look, if I know a particular point, and if I know Except where otherwise noted, textbooks on this site The initial value, or y-intercept, is the output value when the input of a linear function is zero. y Terry is skiing down a steep hill. 2,2 Another approach to representing linear functions is by using function notation. numbers, essentially. It could be a negative We recommend using a citation tool such as. The point at which the input value is zero is the vertical intercept, or y-intercept, of the line. Solving a Linear Function Solving a Linear Function - Part 2 In the previous lesson on functions you learned how to find the slope and write an equation when given a function. the line, then we'd say y minus 6 is equal to m times x The function describing the trains motion is a linear function, which is defined as a function with a constant rate of change, that is, a polynomial of degree 1. So this, by itself, we are in \[\begin{align*} y-4&=-\dfrac{1}{2}(x-6) \\ y-4&=-\dfrac{1}{2}x+3 &\text{Distribute the }-\dfrac{1}{2}. In other words, we can evaluate the function at \(t=12\). [latex]y - 2=-2\left(x+2\right)[/latex]; [latex]y=-2x - 2[/latex]. How to write the rule of a function given the table of values. y y4= is the original distance from the station, 250 meters. Now, in order for this to be a linear equation, the ratio between our change in y and our change in x has to be constant. x+7. Calculate the change of output values and change of input values. negative 2/3 x plus 4, that's slope intercept form. x is negative 2/3 x. An example of slope could be miles per hour or dollars per day. We now have the initial value bb and the slope mm so we can substitute mm and bb into the slope-intercept form of a line. Are the units for slope always The y-intercept is at \((0,b)\). Another way to represent linear functions is visually, using a graph. Table 4 shows the input, p,p, and output, q,q, for a linear function q.q. What was our finishing x ) Linear Equation Calculator - Symbolab Linear equation given two points Calculator - High accuracy - Casio A constant linear function results in a graph that is a horizontal line. The function is increasing because [latex]m>0[/latex]. If Rather than solving for \(m\), we can tell from looking at the table that the population increases by 80 for every 2 weeks that pass. Find the slope. y First, let's look at what you're already given. ff shown in Figure 10. consent of Rice University. Then rewrite the equation in slope-intercept form. x+7. Wed love your input. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph. The population of a city increased from 23,400 to 27,800 between 2008 and 2012. Because we are told that the population increased, we would expect the slope to be positive. Is this function increasing or decreasing? Write the point-slope form of an equation of a line with a slope of 3 that passes through the point [latex]\left(6,-1\right)[/latex]. We can use algebra to rewrite the equation in the slope-intercept form. and we want to subtract from that our starting x value. Now we can use the slope we found and the coordinates of one of the points to find the equation for the line. [latex]\begin{array}{l}y-{y}_{1}=m\left(x-{x}_{1}\right)\\ y - 1=2\left(x - 4\right)\end{array}[/latex]. y=2x9. Interpret slope as a rate of change. We also know one point, so we know \(x_1=6\) and \(y_1 =1\). Posted 11 years ago. C( a. The point (-3, 6) that Sal used to find the equation clearly is not on the y-axis, so it can not be the y-intercept for the line. Notice the graph is a line. As noted earlier, the order in which we write the points does not matter when we compute the slope of the line as long as the first output value or y-coordinate used corresponds with the first input value or x-coordinate used. Write a Linear Equation Given a Table - YouTube +3 What is her rate in miles per hour? 3 and 6. It carries passengers comfortably for a 30-kilometer trip from the airport to the subway station in only eight minutes. Is the initial value always provided in a table of values like Table \(\PageIndex{1}\)? Now we will learn another way to write a linear function called point-slope form which is given below: yy1 = m(xx1) y y 1 = m ( x x 1) where m m is the slope of the linear function and (x1,y1) ( x 1, y 1) is any point which satisfies the linear function. +3 f(x)= The given information gives us two input-output pairs: (3,760)(3,760) and (5,920).(5,920). and Linear equation given two points Calculator - High accuracy calculation Linear equation given two points Calculator Home / Mathematics / Plane geometry Calculates the linear equation, distance and slope given two points. ) If you see an input of 0, then the initial value would be the corresponding output. A citys population in the year 1960 was 287,500. 5). (4,3) A third method of representing a linear function is through the use of a table. So and We can use these points to calculate the slope. ( Write the linear model. If we wanted to then rewrite the equation in slope-intercept form, we apply algebraic techniques. How To: Given THE graph of A linear function, find the equation to describe the function. Suppose, for example, we know that a line passes through the points Write the point-slope form of an equation of a line that passes through the points [latex]\left(-1,3\right)[/latex] and [latex]\left(0,0\right)[/latex]. point slope form. have this 2/3 x on the right-hand side, this As of 1990, average annual income was $23,286. 3 We go through two different examples for writing the equatio. ) We can then use the points to calculate the slope. to that point, what happened to x? Want to cite, share, or modify this book? f(5)=4, Then, determine whether the graph of the function is increasing, decreasing, or constant. The population increased by 27,80023,400=4,400 and that these guys cancel out-- is equal to 4. This videos shows how to write the equation of a linear function using two points. coordinates of a specific point through which the line passes. y= Every month, he adds 15 new songs. Note in function notation two corresponding values for the output y1 y1 and y2y2 for the function ). Direct link to pi expert's post what is the point of the , Posted a month ago. Up until now, we have been using the slope-intercept form of a linear equation to describe linear functions. Restate this function in words. The given information gives us two input-output pairs: \((3,760)\) and \((5,920)\). The rate of change, or slope, is 0.434 PSI per foot. , y Here, we will learn another way to write a linear function, the point-slope form. slope-intercept form of a line: \(f(x)=mx+b\), slope: \(m=\dfrac{\text{change in output (rise)}}{\text{change in input (run)}}=\dfrac{{\Delta}y}{{\Delta}x}=\dfrac{y_2-y_1}{x_2-x_1}\), point-slope form of a line: \(yy_1 =m(x-x_1)\). Ask yourself what numbers can be input to the function, that is, what is the domain of the function? Both equations, 2 A clothing business finds there is a linear relationship between the number of shirts, n,n, it can sell and the price, p,p, it can charge per shirt. [latex]\frac{4,400\text{ people}}{4\text{ years}}=1,100\text{ }\frac{\text{people}}{\text{year}}[/latex]. The input consists of non-negative real numbers. Keep in mind that the slope-intercept form and the point-slope form can be used to describe the same function. Use the model to make a prediction by evaluating the function at a given x-value. For example, suppose we are given the equation [latex]y - 4=-\frac{1}{2}\left(x - 6\right)[/latex] which is in point-slope form. This means that the rate of change is 80 rats per 2 weeks, which can be simplified to 40 rats per week. D Table 1 relates the number of rats in a population to time, in weeks. However, we often need to calculate the slope given input and output values. I think it is the easiest because you can easily graph it, also if you need to change it into the other formulas it can be done easily. [latex]\begin{array}{l}{m}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\hfill \\ \text{}{m}=\frac{7 - 1}{8 - 5}\hfill \\ \text{}{m}=\frac{6}{3}\hfill \\ \text{}{m}=2\hfill \end{array}[/latex]. ( To restate the function in words, we need to describe each part of the equation. Is this function increasing or decreasing? Example 3.3.2: Finding the Domain of a Function. A clown at a birthday party can blow up . Given a word problem that includes two pairs of input and output values, use the linear function to solve a problem. m Find the change in population per year if we assume the change was constant from 2009 to 2012. Notice that the graph of the train example is restricted, but this is not always the case. The costs that can vary include the cost to produce each item, which is $37.50 for Ben. To find the rate of change, we divide the change in output by the change in input. Pre-Calculus - Write a linear function using points - YouTube Write the equation of a linear function given two points and a slope Calculate and Interpret Slope In the examples we have seen so far, we have had the slope provided for us. If we want to rewrite the equation in the slope-intercept form, we would find. are, point slope form, let's say the point x1, y1 are, 2 is the monthly charge, in dollars. [latex]\begin{array}{lll}y - 1=\frac{1}{3}\left(x - 0\right)\hfill & \hfill \\ y - 1=\frac{1}{3}x\hfill & \text{Distribute the }\frac{1}{3}.\hfill \\ \text{}y=\frac{1}{3}x+1\hfill & \text{Add 1 to each side}.\hfill \end{array}[/latex]. Is this function increasing or decreasing? is a function of the time Direct link to Someone's post This is more of a questio, Posted 19 hours ago. As the time (input) increases by 1 second, the corresponding distance (output) increases by 83 meters. So the first thing we want to do *Which is better to use and which is easier to use?*. Write the point-slope form of an equation. We can substitute the initial value and the rate of change into the slope-intercept form of a line. Substitute the slope and the coordinates of one of the points into the point-slope form. To find the rate of change, we divide the change in output by the change in input. intercept form, we just have to add the 6 to both sides so (8,2) I'm just saying, if we go from ( Recall that the slope measures steepness. The initial value of the dependent variable 1 To log in and use all the features of Khan Academy, please enable JavaScript in your browser. That information may be provided in the form of a graph, a point and a slope, two points, and so on. and b ) Let use (0, 1) for our point. my algebra teacher wants me to graph it without putting it into slope intercept form. y-intercept-- where does the line intersect the y-axis-- If we wanted to rewrite the equation in slope-intercept form, we apply algebraic techniques. Yes. 2 m The point-slope equation of the line is \(y_21=2(x_25)\). Some recent studies suggest that a teenager sends an average of 60 texts per day. where \(b\) is the initial or starting value of the function (when input, \(x=0\)), and \(m\) is the constant rate of change, or slope of the function. Determine whether a linear function is increasing, decreasing, or constant. When she plants 30 stalks, each plant yields 30 oz of beans. and We can then use the points to calculate the slope.

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