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  • Caroline Schreier

Linear Functions: How to Graph

Graphing equations allows us to have a better understanding of an equation, and what it represents. Let's look at the example below:


Graph the equation y = .5x + 1


Step 1: Plot the y-intercept. Remember that in the equation y = mx +b, b is the y-intercept. Also remember that the y-intercept is the point on the graph where x = 0. In this example, the y-intercept is at (0,1).


Step 2: Use the rate of change (m) to plot points. In this equation, the rate of change, m, is .5 (or 1/2). This means that for every one it goes up, it must go two right. Knowing this, start at the y-intercept and go up one, right two, and plot the point there. Do this as many times as you want (as you get more comfortable with graphing, you won't need to plot as many points).


After this, go back to the y-intercept. To find points in the opposite direction, count down one, left two, and plot points as you go.


Step 3: Draw a line through all the points, extend it, and draw an arrow on either end.


Now try some practice problems on your own: (You can do this by printing out graph paper or drawing your own coordinate plane and estimating!)

1) Graph the equation: y = 3x - 1

2) Graph the equation: y = -2x + 3

3) Graph the equation: y = .75x - 2


Answers:


1) Graph:










Explanation: You can see from the equation that the y-intercept (b) is (0,-1). Once you have plotted this point, look at the rate of change (m), which here is 3. This means that for every 3 units up, you should go 1 to the right. Start at the y-intercept and go up 3, right 1 until you have enough points graphed. Then go back to the y-intercept and go in the opposite direction: down 3, left 1. Connect all your points, and your graph should look like this!


2) Graph:















Explanation: First, find the y-intercept (b) in the equation. In this example, the y-intercept is (0,3). Once you have plotted that point, look at the rate of change (m), which in this problem is -2. This means that for every 2 units down, go right 1 unit (or for every 2 units up, go left 1 unit). Start at the y-intercept and count down 2, right 1. Once you've plotted enough points, go back to the y-intercept and count up 2, left one. Connect all the points and your graph should look like the one above!

3) Graph:












Explanation: Start by looking at the y-intercept (b), which in this equation is (0,-2). Once you've plotted that point, find the rate of change (m) in the equation, which here is .75. To be able to plot points from this, it's easiest to know what that decimal is as a fraction. As a fraction, .75 is 3/4, which means that for every 3 units up, you should go 4 units to the right. Start from the y-intercept, and when you've plotted enough points in that direction, go back to the y-intercept and go the opposite way, plotting a point every 3 units down and 4 to the left. Finally, draw a line through the points, and you're done!


Made using Desmos.com and Google Images.