Question

a line passes through the point (-8, 4) and has a slope of $-\frac{3}{4}$. write an equation in slope - intercept form for this line.

Explanation:

Step1: Recall point-slope formula

The point-slope form is $y - y_1 = m(x - x_1)$, where $m=-\frac{3}{4}$, $x_1=-8$, $y_1=4$.

Step2: Substitute values into formula

$y - 4 = -\frac{3}{4}(x - (-8))$
Simplify the right-hand side:
$y - 4 = -\frac{3}{4}(x + 8)$

Step3: Expand and solve for y

$y - 4 = -\frac{3}{4}x - 6$
Add 4 to both sides:
$y = -\frac{3}{4}x - 6 + 4$

Step4: Simplify the constant term

$y = -\frac{3}{4}x - 2$

Answer:

$y = -\frac{3}{4}x - 2$