Question

what is the equation of the line that passes through the point $(8, 3)$ and has a slope of $-\frac{1}{4}$?

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)=(8,3)$ and $m=-\frac{1}{4}$.
$y - 3 = -\frac{1}{4}(x - 8)$

Step2: Simplify to slope-intercept form

Distribute the slope and isolate $y$.
$y - 3 = -\frac{1}{4}x + 2$
$y = -\frac{1}{4}x + 2 + 3$

Answer:

$y = -\frac{1}{4}x + 5$