Answer
$\color{blue}{y=-\frac{1}{2}x-\frac{3}{2}}$
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 $-1$ (negative reciprocals of each other).
The line we are looking for is perpendicular to $y=2x-3$ (whose slope is $2$).
This means that the line has a slope of $-\frac{1}{2}$ (since $-\frac{1}{2}(2)=-1$).
Thus, a tentative equation of the line we are looking for is:
$y=-\frac{1}{2}x+b$
To find the value of $b$, substitute the x and y values of the given point to obtain:
$y=-\frac{1}{2}x+b
\\-2 = -\frac{1}{2}(1)=b
\\-2 = -\frac{1}{2} + b
\\-2+\frac{1}{2}=b
\\-\frac{4}{2}+\frac{1}{2}=b
\\-\frac{3}{2}=b$
Thus, the equation of the line is:
$\color{blue}{y=-\frac{1}{2}x-\frac{3}{2}}$
