Question

what is the equation of the line that passes through the point $(-4, 8)$ and has a slope of $-1?$

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $m=-1$, $x_1=-4$, $y_1=8$.
$y - 8 = -1(x - (-4))$

Step2: Simplify the equation

Simplify the right-hand side.
$y - 8 = -1(x + 4)$

Step3: Expand and isolate $y$

Distribute $-1$ and solve for $y$.
$y - 8 = -x - 4$
$y = -x - 4 + 8$
$y = -x + 4$

Answer:

$y = -x + 4$