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.
(7,1) and (7,9)
select the correct choice below and fill in the answer box within your choice.
a. the slope is \boxed{}. (simplify your answer.)
b. the slope is undefined.
indicate whether the line through the points rises, falls, is horizontal, or is vertical.
the line is vertical.
the line rises from left to right.
the line falls from left to right.
the line is horizontal.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
For the points \((7,1)\) and \((7,9)\), we have \( x_1 = 7\), \( y_1 = 1\), \( x_2 = 7\), \( y_2 = 9 \).

Step2: Calculate the slope

Substitute into the formula: \( m=\frac{9 - 1}{7 - 7}=\frac{8}{0} \). Division by zero is undefined, so the slope is undefined.

Step3: Determine the line's nature

When the slope is undefined, the line is vertical (since all points have the same \( x \)-coordinate, \( x = 7 \), which is a vertical line).

Answer:

For the slope: B. The slope is undefined.
For the line's nature: The line is vertical.