Question

find the slope of a line perpendicular to the line whose equation is 10x - 12y = -24. fully simplify your answer.

Explanation:

Step1: Transform to slope - intercept form

First, transform the equation $10x - 12y=-24$ to $y = mx + b$ form.
$10x-12y=-24$ can be rewritten as $12y = 10x + 24$, then $y=\frac{10}{12}x+\frac{24}{12}=\frac{5}{6}x + 2$. The slope of this line $m_1=\frac{5}{6}$.

Step2: Use the perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of the perpendicular line be $m_2$. Then $m_1\times m_2=-1$.
Since $m_1 = \frac{5}{6}$, we have $\frac{5}{6}\times m_2=-1$. Solving for $m_2$, we get $m_2=-\frac{6}{5}$.

Answer:

$-\frac{6}{5}$