The following formula is used to calculate a rate of change:
\[ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \]
Where:
The rate of change of a line is often referred to as the slope, or rise over run. It’s a measure of how quickly a line is changing in the y-direction with every step in the x-direction. This can also be done using a similar formula, but substituting x and y in the formula. This results in the rate of change of x with respect to y, or run over rise.
Let's say we have two points on a line: (2, 3) and (5, 11). To find the rate of change, we can use the formula:
\[ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values, we get:
\[ \text{Rate of Change} = \frac{11 - 3}{5 - 2} = \frac{8}{3} \approx 2.67 \]
Therefore, the rate of change for the line passing through the points (2, 3) and (5, 11) is approximately 2.67.
