which is the slope of a line that is perpendicular to the line that passes through the points $(-9,-4)$ and…

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

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

Answer

Explanation:

Step1: Calculate the slope of the line passing through the two points

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Given ((x_1,y_1)=(-9,-4)) and ((x_2,y_2)=(3,4)), then (m=\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). Let (m_1=\frac{2}{3}), then (m_2=-\frac{3}{2}) (since (\frac{2}{3}\times m_2=-1), solving for (m_2) gives (m_2=-\frac{3}{2})).

Answer:

(-\frac{3}{2}) (corresponding to the first option)