Question

which equation represents a line which is perpendicular to the line $4x + 3y = -24$?
answer
$y = \frac{4}{3}x - 7$ $y = -\frac{3}{4}x - 4$
$y = \frac{3}{4}x + 4$ $y = -\frac{4}{3}x - 5$

Explanation:

Step1: Convert to slope-intercept form

Rearrange $4x + 3y = -24$ to $y = mx + b$:
$$3y = -4x -24$$
$$y = -\frac{4}{3}x - 8$$
The slope of the given line is $m_1 = -\frac{4}{3}$.

Step2: Find perpendicular slope

Perpendicular slopes are negative reciprocals:
$$m_2 = \frac{3}{4}$$

Step3: Match with options

Identify the option with slope $\frac{3}{4}$.

Answer:

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