Question

write an equation of the line that passes through (7, 10) and is perpendicular to the line $y = \frac{1}{2}x - 9$.
$y = \square$

Explanation:

Step1: Find perpendicular slope

The slope of $y=\frac{1}{2}x-9$ is $\frac{1}{2}$. Perpendicular slopes multiply to $-1$, so new slope $m = -2$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $(7,10)$ and $m=-2$:
$y - 10 = -2(x - 7)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y - 10 = -2x + 14$
$y = -2x + 14 + 10$
$y = -2x + 24$

Answer:

$y = -2x + 24$