Answer
$y = -x - 1$
Work Step by Step
We know that perpendicular lines are opposite reciprocals of one another, so let us look at the equation of the line first to see if we can determine what the slope is.
$y = x - 5$
This equation is in slope-intercept form and has a slope of $1$.
The opposite reciprocal of $1$ is $-1$. This is the slope of the line we want to find.
We also have a point on this line, so we can use the point-slope form, which is given by the formula $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line:
$y - (-3) = -1(x - 2)$
Simplify:
$y + 3 = -x + 2$
Subtract $3$ from each side of the equation to isolate $y$ on the left side of the equation:
$y = -x - 1$
