Lines and the Coordinate Plane: Slope of a Line

Horizontal and Vertical Lines

Horizontal lines are parallel to the x-axis.  Look at the graph below.

graph of line of y equals 3 with points (negative 1, 3) and (2, 3)

Notice that two points on the line are (-1, 3) and (2, 3).

Apply the formula:

m equals 3 minus 3 divided by 2 minus negative 1, m equals 0 divided by 3, m equals 0

So, the slope of the line is 0.  In fact, all points along a horizontal line will have the same y-coordinate, so the slope of any horizontal line is 0.

What is the slope of a vertical line?

graph of x equals negative 1 with points (negative 1, 2) and (negative 1, negative 3)

(-1, 2) and (-1, -3) are points on the line.

Apply the formula:

m equals negative 2 minus 2 divided by negative 1 minus negative 1, m equals negative 5 divided by 0

Division by 0 is undefined, so the slope of a vertical line is undefined.