Question

the equation of line c is $y = \frac{1}{8}x + 10$. line d is perpendicular to line c and passes through $(-1, 1)$. what is the equation of line d?
write the equation in slope-intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find slope of line d

Perpendicular slopes multiply to -1.
Slope of line c is $\frac{1}{8}$, so slope of line d: $m = -8$

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$
Substitute $m=-8$, $x_1=-1$, $y_1=1$:
$y - 1 = -8(x - (-1))$

Step3: Simplify to slope-intercept

Expand and solve for $y$:
$y - 1 = -8(x + 1)$
$y - 1 = -8x - 8$
$y = -8x - 8 + 1$
$y = -8x - 7$

Answer:

$y = -8x - 7$