## College Algebra (10th Edition)

$\color{blue}{y=-x+3}$
RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where $m$=slope and $b$ = y-intercept. (2) Parallel lines have the same (equal) slopes. Line $L$ is parallel to the line $y=-x$, whose slope is $-1$. Since $L$ is parallel to this line, $L$ also has a slope of $-1$. 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 $(1, 2)$ into the tentative equation above to obtain: $y=-2x+b \\2=-(1) + b \\2+1 = b \\3=b$ Therefore, the equation of line $L$ is $\color{blue}{y=-x+3}$.