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).
Write the equation of the given line in slope-intercept form to obtain:
$2x+y=2
\\y=-2x+2$
The line we are looking for is perpendicular to the line above (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:
$y=\frac{1}{2}x+b
\\0 = \frac{1}{2}(-3)=b
\\0 = -\frac{3}{2} + b
\\0+\frac{3}{2}=b
\\\frac{3}{2}=b$
Thus, the equation of the line is:
$\color{blue}{y=\frac{1}{2}x+\frac{3}{2}}$
