Question

which equation is perpendicular to $y = 4x - 6$ and passes through point $(8, 12)$?
a. $y = 4x - 20$
b. $y = -\frac{1}{4}x + 14$
c. $y = 4x + 44$
d. $y = \frac{1}{4}x + 10$

Explanation:

Step1: Find slope of perpendicular line

Slope of given line is 4. Perpendicular slope is $-\frac{1}{4}$.

Step2: Use point-slope form

Point-slope: $y - y_1 = m(x - x_1)$. Substitute $(8,12)$ and $m=-\frac{1}{4}$: $y - 12 = -\frac{1}{4}(x - 8)$

Step3: Simplify to slope-intercept

$y - 12 = -\frac{1}{4}x + 2$ → $y = -\frac{1}{4}x + 14$

Answer:

B. $y = -\frac{1}{4}x + 14$