Question

find the slope of the line passing through the pair of points or state that the slope is undefined. then indicate whether the line through the points rises, falls, is horizontal, or is vertical.
(7,4) and (-9,4)
select the correct choice below and, if necessary, fill in the answer box within your choice.
a. the slope is 0. (simplify your answer.)
b. the slope is undefined.
indicate whether the line through the points rises, falls, is horizontal, or is vertical.
a. the line rises from left to right.
b. the line is vertical.
c. the line is horizontal.
d. the line falls from left to right.

Explanation:

For the slope calculation:

Step1: Recall the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1 = 7 \), \( y_1 = 4 \), \( x_2=-9 \), \( y_2 = 4 \).

Step2: Substitute the values into the formula

\( m=\frac{4 - 4}{-9 - 7}=\frac{0}{-16}=0 \).

A line with a slope of \( 0 \) is horizontal because the \( y \)-coordinates of the two points are the same, meaning the line is parallel to the \( x \)-axis. A horizontal line does not rise or fall from left to right.

Answer:

The slope is \( 0 \).

For the direction of the line: