Question

(a) find the slope of the line through the pair of points (3,0) and (-2,0), if possible, and (b) based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical. (a) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the slope of the line is. (type an integer or a simplified fraction ) b. the slope is undefined.

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the coordinates

For the points \( (3, 0) \) and \( (-2, 0) \), we have \( x_1 = 3 \), \( y_1 = 0 \), \( x_2=-2 \), \( y_2 = 0 \).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{0 - 0}{-2 - 3}=\frac{0}{-5}=0 \).

For part (b), a slope of 0 means the line is horizontal (since horizontal lines have a slope of 0, and they do not rise or fall from left to right, they are flat).

Answer:

(a):
A. The slope of the line is \( 0 \).