Algebra 2 Common Core

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

Chapter 2 - Functions, Equations, and Graphs - 2-5 Using Linear Models - Practice and Problem-Solving Exercises - Page 98: 31

Answer

$y=x+1$ (red graph) $y=2x-1$ (blue graph)
1557993662

Work Step by Step

Linear equations of the form $y=mx+b$ has a $y$-intercept of $b$ and a slope of $m.$ Hence, the given equation, $ y=x+1 $ has \begin{align*} y\text{-intercept: }& 1 \\\text{Slope: }& 1\text{ or } \dfrac{1}{1} .\end{align*} To graph the equation, start at the $y-$intercept of $( 0,1 )$. Then use the notion of the slope as $\dfrac{rise}{run}.$ Since the slope is $ \dfrac{1}{1} ,$ then $rise= 1 $ and $run= 1 .$ Hence, from the $y$-intercept, go up by $rise= 1 $ unit then go to the right by $run= 1 $ unit. This results to the point $( 1,2 )$. By connecting this point and the $y$-intercept, the graph of $ y=x+1 $ (red graph) is determined. Similarly, the other given equation, $ y=2x-1 $ has \begin{align*} y\text{-intercept: }& -1 \\\text{Slope: }& 2\text{ or } \dfrac{2}{1} .\end{align*} The $y-$intercept is $( 0,-1 )$. Using the notion of the slope as $\dfrac{rise}{run},$ then $rise= 2 $ and $run= 1 .$ Hence, from the $y$-intercept, go up by $rise= 2 $ units then go to the right by $run= 1 $ unit. This results to the point $( 1,1 )$. By connecting this point and the $y$-intercept, the graph of $ y=2x-1 $ (blue graph) is determined.
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