Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 2 - Functions, Equations, and Graphs - 2-3 Linear Functions and Slope-Intercept Form - Practice and Problem-Solving Exercises - Page 79: 40


Refer to the image below for the graph.

Work Step by Step

First, we need to write this equation in slope-intercept form to make the slope and y-intercept clear. To isolate $y$ and its coefficient, we add $2x$ to both sides, giving $3y=2x-12$. To completely isolate $y$, we divide both sides by 3, giving $y=\frac{2}{3}x-\frac{12}{3} \\y=\frac{2}{3}x-4$. To graph the line, we graph two points using the equation and then connect the dots. One point we can use is the y-intercept, so $(0,-4)$. Another point we can use is if $x=3$ (any value for $x$ works). We substitute that into $y=\frac{2}{3}x-4$ to get $y=\frac{2}{3}(3)-4=-2$ The point is $(3,-2)$. Plot the two points then connect them using a line. (refer to the attached image above for the graph)
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