Rate of change is the change in the dependent quantity for each one-unit change in the independent quantity, represented by the slope . From a graph of a linear relation, it can be determined using two points and interpreted by its sign, magnitude, and units—including positive, negative, zero, or fractional rates—while recognizing that visual steepness depends on the graph’s scales; instantaneous rates and advanced analysis of nonlinear graphs are not included.
For a straight-line graph, the rate of change tells how much the -value changes when the -value increases by 1. It is also called the slope.
Use the formula
Here, means “change in.”
Example: A graph shows the amount of money in a savings account over time. Two points on the line are and , where is time in months and is money in dollars.
Step 1: Choose two points.
Let
Step 2: Find the change in .
The amount of money increases by $8.
Step 3: Find the change in .
The time increases by months.
Step 4: Divide the changes.
Step 5: Include the units and interpret the answer.
The rate of change is
This means the account balance increases by $2 for every 1-month increase in time.
A positive rate means the graph rises from left to right. A negative rate means it falls, and a rate of means it is horizontal. Always calculate the rate using two points and the changes in their coordinates rather than judging only by how steep the line looks, because the graph’s scales can affect its appearance.
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