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

Explanation:

Step1: Rewrite the line in slope - intercept form

First, rewrite $10x−12y = - 24$ as $y=mx + b$ form. Starting with $10x−12y=-24$, we get $-12y=-10x - 24$. Then $y=\frac{10}{12}x + 2=\frac{5}{6}x+2$. 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 $- 1$, i.e., $m_1\times m_2=-1$. Let the slope of the perpendicular line be $m_2$. We know $m_1 = \frac{5}{6}$, so $\frac{5}{6}\times m_2=-1$. Solving for $m_2$, we get $m_2=-\frac{6}{5}$.

Answer:

$-\frac{6}{5}$