Question

write an equation of the line that passes through (-4, -1) and is perpendicular to the line $y = \frac{4}{3}x + 6$.

$y = \square$

Explanation:

Step1: Find perpendicular slope

The slope of $y=\frac{4}{3}x+6$ is $\frac{4}{3}$. Perpendicular slope is the negative reciprocal: $m = -\frac{3}{4}$

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=-\frac{3}{4}$, $x_1=-4$, $y_1=-1$:
$y - (-1) = -\frac{3}{4}(x - (-4))$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y + 1 = -\frac{3}{4}(x + 4)$
$y + 1 = -\frac{3}{4}x - 3$
$y = -\frac{3}{4}x - 4$

Answer:

$y = -\frac{3}{4}x - 4$