Question

find the slope of the line satisfying the following conditions. horizontal, through (2,6) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the slope is (type an integer or a simplified fraction ) b. the slope is undefined.

Explanation:

Step1: Recall slope of horizontal line

A horizontal line has a slope of 0 because the change in \( y \)-values (\( \Delta y \)) between any two points on the line is 0. The slope formula is \( m = \frac{\Delta y}{\Delta x} \), and for a horizontal line, \( \Delta y = 0 \), so \( m = \frac{0}{\Delta x}=0 \) (where \( \Delta x
eq0 \)).

Step2: Confirm with the given point

The line is horizontal and passes through \( (2, 6) \). All points on a horizontal line have the same \( y \)-coordinate. So, for any two points on this line, the difference in \( y \)-coordinates is 0, leading to a slope of 0.

Answer:

A. The slope is \( 0 \)