Question

1. write the equation of the line that is perpendicular to y = 8x + 4 and passes through the point (16, -4).

Explanation:

Step1: Find perpendicular slope

The slope of $y=8x+4$ is $8$. Perpendicular slope is the negative reciprocal: $m = -\frac{1}{8}$

Step2: Substitute point into slope-intercept form

Use $y = mx + b$, substitute $(x,y)=(16,-4)$ and $m=-\frac{1}{8}$:
$-4 = -\frac{1}{8}(16) + b$

Step3: Solve for y-intercept $b$

Calculate $-\frac{1}{8}(16) = -2$, so:
$-4 = -2 + b$
$b = -4 + 2 = -2$

Step4: Write final line equation

Substitute $m=-\frac{1}{8}$ and $b=-2$ into $y=mx+b$.

Answer:

$y = -\frac{1}{8}x - 2$