Question

find the equation of a line perpendicular to $y = 2x - 6$ that passes through the point $(-8, -2)$. answer $x - 2y = -4$ $y = \frac{1}{2}x - 6$ $y = -\frac{1}{2}x - 6$ $-2x + y = 14$

Explanation:

Step1: Find perpendicular slope

The slope of $y=2x-6$ is $2$. Perpendicular slope is $-\frac{1}{2}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$
Substitute $m=-\frac{1}{2}$, $x_1=-8$, $y_1=-2$:
$y - (-2) = -\frac{1}{2}(x - (-8))$

Step3: Simplify the equation

$y + 2 = -\frac{1}{2}(x + 8)$
$y + 2 = -\frac{1}{2}x - 4$
$y = -\frac{1}{2}x - 6$

Step4: Verify matching option

The simplified equation matches the third option.

Answer:

$y = -\frac{1}{2}x - 6$