## College Algebra (10th Edition)

$\color{blue}{y=x-7}$
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 $-1$. The line we are looking for the equation of is perpendicular to the line $\\x+y=2$. Converting this equation into slope-intercept form gives: $x+y=2 \\y=-x+2$ The slope of this line is $-1$. This means that the slope of the line perpendicular to this line is $1$ (since $-1(1) = -1$). Thus, the tentative equation of the line is: $y=1(x) + b \\y=x+b$ To find the value of $b$, substitute the x and y values of the point $(4, -3)$ into the tentative equation above to obtain: $y=x+b \\-3=4+b \\-3-4=b \\-7=b$ Thus, the equation of the line is $\color{blue}{y=x-7}$.