Question

write an equation of the line passing through (-4,7) and having slope -8. give the answer in slope - intercept form. the equation of the line in slope - intercept form is \square.

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, $x_1=-4$, $y_1 = 7$ and $m=-8$.
Substitute these values into the point - slope form: $y - 7=-8(x - (-4))$, which simplifies to $y - 7=-8(x + 4)$.

Step2: Convert to slope - intercept form

Slope - intercept form is $y=mx + b$. We expand the right - hand side of the equation from Step 1:
$y-7=-8x-32$
Then, add 7 to both sides of the equation to solve for $y$:
$y=-8x-32 + 7$
$y=-8x-25$

Answer:

$y=-8x - 25$