Question

question
find the slope of a line perpendicular to the line whose equation is (4x - 6y = -24). fully simplify your answer.
answer

Explanation:

Step1: Rewrite in slope-intercept form

Start with the given equation:
$$4x - 6y = -24$$
Isolate $y$:
$$-6y = -4x -24$$

Step2: Solve for y to find slope

Divide all terms by $-6$:
$$y = \frac{-4}{-6}x + \frac{-24}{-6}$$
Simplify the fractions:
$$y = \frac{2}{3}x + 4$$
The slope of the given line is $\frac{2}{3}$.

Step3: Find perpendicular slope

Perpendicular slopes are negative reciprocals. Take the negative reciprocal of $\frac{2}{3}$:
$$m_{\perp} = -\frac{3}{2}$$

Answer:

$\boldsymbol{-\frac{3}{2}}$