Question

find the slope of the line satisfying the following conditions. vertical through (9, -7) select the correct choice below and fill in any answer boxes within your choice. a. the slope is (type an integer or a simplified fraction.) b. the slope is undefined.

Explanation:

Step1: Recall slope definition

The slope \( m \) of a line is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line.

Step2: Analyze vertical line

For a vertical line, all points on the line have the same \( x \)-coordinate. So, if we take two points \( (9, - 7) \) and \( (9,y) \) (where \( y
eq - 7 \)) on the vertical line, then \( x_2 - x_1=9 - 9 = 0 \).
When we try to calculate the slope using the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \), we get a division by zero (since \( x_2 - x_1 = 0 \)), and division by zero is undefined in mathematics.

Answer:

B. The slope is undefined.