Question

find the equation of a line perpendicular to $y = -4x - 1$ that passes through the point $(4, 5)$.

answer

$\bigcirc$ $y = -\frac{1}{4}x + 4$ $\bigcirc$ $4x + y = 21$

$\bigcirc$ $y = 4x - 1$ $\bigcirc$ $-x + 4y = 16$

Explanation:

Step1: Find perpendicular slope

The slope of $y=-4x-1$ is $-4$. The slope of a perpendicular line is the negative reciprocal: $m=\frac{1}{4}$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $(x_1,y_1)=(4,5)$ and $m=\frac{1}{4}$:
$y-5=\frac{1}{4}(x-4)$

Step3: Simplify to slope-intercept

Expand and rearrange:
$y-5=\frac{1}{4}x - 1$
$y=\frac{1}{4}x + 4$

Step4: Convert to standard form

Multiply through by 4:
$4y=x + 16$
Rearrange to match options:
$-x + 4y=16$

Answer:

$-x + 4y = 16$