In the previous section, you learned the definition of slope to be as follows:

Rate of Change = change in y over change in x Change in y Change in x = slope

Graphically, the slope of a line can be represented using a change in the vertical direction and a change in the horizontal direction.

graph of line with a slope of five eights, showing a vertical change of 5 units upward and a horizontal change of 8 units to the right

Given two points (x1, y1) and (x2, y2), the slope of a line can be determined using the formula below.

Slope of a line = m = y2y1 x2x1 ,
where m represents the slope of the line.

In the slope formula, y2 - y1 represents the change in y, while x2x1 represents the change in x. Let’s practice using the slope formula with the interactive below.


Directions: Find the slope of the line connecting the points (-4, 7) and (-3, -1). Simplify the numerator and denominator in order to determine the change in the vertical direction and the change in the horizontal direction.

Interactive exercise. Assistance may be required. Drag the numbers into the appropriate place in the formula.


Practice

Determine the slope of the line connecting the two points given.

  1. (3, 5) and (8, 10)

    Interactive popup. Assistance may be required.

    Need a hint?

    Use the slope formula where the point (3, 5) is (x1, y1), and the point (8, 10) is (x2, y2).Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    m = y2y1 x2x1 = 10 – 5 8 – 3 = 5 over 5 5 5 = 1 Close Pop Up
  2. (-3, 7) and (5, -2)

    Interactive popup. Assistance may be required.

    Need a hint?

    Use the slope formula where the point (-3, 7) is (x1, y1), and the point (5, -2) is (x2, y2).Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    m = y2y1 x2x1 = -2 – 7 5 – (-3) = -9 over 8 -9 8 = -9 over 8 - 9 8 Close Pop Up
  3. (2d, 7d) and (3d, d)

    Interactive popup. Assistance may be required.

    Need a hint?

    Use the slope formula where the point (2d, 7d) is (x1, y1), and the point (3d, d) is (x2, y2). Be sure to simplify by canceling common factors in the numerator and denominator.Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    Close Pop Up