Question

complete the sentence below.
the slope of a vertical line is ____, the slope of a horizontal line is ____.
the slope of a vertical line is
, the slope of a horizontal line is

Explanation:

Step1: Recall slope formula

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

Step2: Analyze vertical line

For a vertical line, \( x_1 = x_2 \), so \( x_2 - x_1 = 0 \). Division by zero is undefined, so slope of vertical line is undefined.

Step3: Analyze horizontal line

For a horizontal line, \( y_1 = y_2 \), so \( y_2 - y_1 = 0 \). Then \( m=\frac{0}{x_2 - x_1}=0 \) (as \( x_2
eq x_1 \) for non - vertical line), so slope of horizontal line is 0.

Answer:

The slope of a vertical line is undefined; the slope of a horizontal line is 0.