Question

which is the slope of a line that is perpendicular to the line that passes through the points (-9, -4) and (3, 4)?
a. $\frac{3}{2}$
b. $-\frac{2}{3}$
c. $-\frac{3}{2}$
d. $\frac{2}{3}$

Explanation:

Step1: Calculate the slope of the given line.

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-9,-4)$ and $(x_2,y_2)=(3,4)$. Then $m_1=\frac{4 - (-4)}{3-(-9)}=\frac{4 + 4}{3 + 9}=\frac{8}{12}=\frac{2}{3}$.

Step2: Find the slope of the perpendicular line.

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$. So $m_2=-\frac{1}{m_1}$. Since $m_1 = \frac{2}{3}$, then $m_2=-\frac{3}{2}$.

Answer:

C. $-\frac{3}{2}$