Question

find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points (-3,9) and (0,0)
(a) select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the slope of the parallel line is □. (type an integer or a simplified fraction.)
b. the slope of the parallel line is undefined.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line. Here, \((x_1,y_1)=(-3,9)\) and \((x_2,y_2)=(0,0)\).

Step2: Substitute the values into the formula

Substitute \(x_1=-3,y_1 = 9,x_2=0,y_2 = 0\) into \(m=\frac{y_2 - y_1}{x_2 - x_1}\), we get \(m=\frac{0 - 9}{0-(-3)}=\frac{-9}{3}=- 3\).

Answer:

A. The slope of the parallel line is \(-3\)