## College Algebra (10th Edition)

Published by Pearson

# Chapter 2 - Section 2.3 - Lines - 2.3 Assess Your Understanding: 46

#### Answer

$\color{blue}{y=x+2}$

#### Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where $m$=slope and $b$ = y-intercept. (2) Perpendicular lines have slopes whose product is $-1$. Line $L$ is perpendicular to the line $y=-x$, whose slope is $-1$. Since $L$ is perpendicular to this line, then $L$ has a slope of $1$ (since $-1 \cdot 1=-1$) Thus, the tentative equation of the line is $y=x+b$. To find the value of $b$, substitute the x and y values of the point $(-1, 1)$ into the tentative equation above to obtain: $y=x+b \\1=-1 + b \\1+1=b \\2=b$ Therefore, the equation of line $L$ is $\color{blue}{y=x+2}$.

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