Question

Sketch a graph of a vertical line. Use the definition of slope (m=\frac{y_2-y1}{x_2-x_1}) to explain how the slope of the line is classified.Sketch a graph of a horizontal line. Use the definition of slope (m=\frac{y_2-y1}{x_2-x_1}) to explain how the slope of the line is classified.

Answer 1

To graph a vertical line, plot a point that the line passes through, and then draw a line through the point which is parallel to the y-axis.

A vertical line passing through a point is shown below:

Next, choose two points on the line to calculate the slope.

Two points on the line are (2,2) and (2,5).

Substitute (x1,y1)=(2,2) and (x2,y2)=(2,5) into the equation for the definition of a slope:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{2-2}=\frac{3}{0}=\text{undefined.}$

It follows that the slope of a vertical line is undefined.