# How Do You Find the Rate of Change?

To find the rate of change of a line, determine the vertical change and the horizontal change. Write the rate of change as a fraction, placing the vertical change over the horizontal change. Finally, simplify the fraction, if necessary.

1. Find the vertical change

Write down the points that you are given, or graph the line to find two x-values and two y-values. Subtract the second y-value from the first y-value to find the vertical change.

2. Find the horizontal change

Subtract the second x-value from the first x-value to find the horizontal change.

3. Find the rate of change

Write the value of the vertical change over the value of the horizontal change. Simplify the fraction if there are two negative values or if the numerator and the denominator share a common factor. If given the equation y= 2x+1, graph the line to find two points; (-2, -3) and (1, 3) are two points on the line. To find the vertical change, perform 3 minus -3, which is equal to 6. To find the horizontal change, perform 1 minus (-2), which is equal to 3. The rate of change is equal to 6/3, or 2. Check the answer by performing the method using two other points on the line. The rate of change of 2 is the same for all points along y=2x+1.