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 78: 34


graph of $y-3=-2x$:

Work Step by Step

In the form $y=mx+b,$ the given equation, $ y-3=-2x ,$ is equivalent to \begin{align*} y-3+3&=-2x+3 \\ y&=-2x+3 .\end{align*} Using $y=mx+b$ or the Slope-Intercept Form of linear equations, where $b$ is the $y$-intercept and $m$ is the slope, the equation above has the following characteristics: \begin{align*} \text{$y$-intercept: }& 3 \\ \text{Slope: }& -2\text{ or }\dfrac{-2}{1} .\end{align*} To graph the slope-intercept equation above, start at the $y$-intercept. This corresponds to the point $ (0,3) $. Using the notion of the slope as $\dfrac{rise}{run},$ then $rise= -2 $ and $run= 1 .$ From the $y$-intercept, go $\text{ down }$ by $rise= -2 $ units and then go to the right by $run= 1 $ units. This results to the point $ (1,1) .$ Connecting this point and the $y$-intercept gives the graph of the given equation.
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