Question

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

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1=-4$, $y_1 = 8$ and $m=-1$.

Step2: Substitute values into point - slope form

Substitute $x_1=-4$, $y_1 = 8$ and $m = - 1$ into the point - slope form:
$y-8=-1(x - (-4))$
Simplify the right - hand side: $y - 8=-1(x + 4)$

Step3: Convert to slope - intercept form (optional, but to get the equation in $y=mx + b$ form)

Expand the right - hand side: $y-8=-x - 4$
Add 8 to both sides of the equation: $y=-x - 4+8$
Simplify the right - hand side: $y=-x + 4$

Answer:

$y=-x + 4$ (or in standard form $x + y=4$)