Question

point a(-5, 2) and point b(3, 4) are graphed to form $overline{ab}$. what is the slope of a line perpendicular to $overline{ab}$?
f. 1/2
g. 4
h. -4
j. -1

Explanation:

Step1: Calculate slope of $\overline{AB}$

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $A(-5,2)$ and $B(3,4)$, we have $x_1=-5,y_1 = 2,x_2=3,y_2 = 4$. Then $m_{AB}=\frac{4 - 2}{3-(-5)}=\frac{2}{8}=\frac{1}{4}$.

Step2: Find slope of perpendicular line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular line be $m_p$. Then $m_{AB}\times m_p=-1$. Substituting $m_{AB}=\frac{1}{4}$, we get $\frac{1}{4}\times m_p=-1$, so $m_p=-4$.

Answer:

H. -4