Question

question 23 of 40
what is the equation of a line that is perpendicular to $y=4x+5$ and passes through the point $(8, 3)$?
a. $y=-\frac{1}{4}x-8$
b. $y=-\frac{1}{4}x+3$
c. $y=\frac{1}{4}x+1$
d. $y=-\frac{1}{4}x+5$

Explanation:

Step1: Find perpendicular slope

The slope of $y=4x+5$ is $4$. Perpendicular slope is the negative reciprocal: $m=-\frac{1}{4}$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $(x_1,y_1)=(8,3)$ and $m=-\frac{1}{4}$:
$y-3=-\frac{1}{4}(x-8)$

Step3: Simplify to slope-intercept form

Expand and solve for $y$:
$y-3=-\frac{1}{4}x + 2$
$y=-\frac{1}{4}x + 2 + 3$
$y=-\frac{1}{4}x + 5$

Answer:

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