Question

a line passes through the point (8, -5) and has a slope of $-\frac{3}{4}$. write an equation in slope - intercept form for this line.

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)=(8, -5)$ and $m=-\frac{3}{4}$.
$y - (-5) = -\frac{3}{4}(x - 8)$

Step2: Simplify the left side

$y + 5 = -\frac{3}{4}(x - 8)$

Step3: Distribute the slope

$y + 5 = -\frac{3}{4}x + 6$

Step4: Isolate y to solve

Subtract 5 from both sides.
$y = -\frac{3}{4}x + 6 - 5$

Answer:

$y = -\frac{3}{4}x + 1$