Find rates from coordinate graphs
Finding rates from coordinate graphs is a Grade 7 ratio and proportional reasoning skill in Big Ideas Math, Course 2. On a proportional relationship graph, the rate (unit rate) equals the slope: rise divided by run between any two points. To find the rate, select two points on the line, compute the change in y (vertical) divided by the change in x (horizontal). For a graph showing distance over time, two points (2, 50) and (4, 100) give a rate of (100−50)/(4−2) = 25 miles per hour. For non-proportional relationships, the rate between two specific points represents an average rate of change over that interval.
Key Concepts
To find a rate from a graph, choose any point $(x, y)$ and calculate: $$\text{Rate} = \frac{y\text{ coordinate}}{x\text{ coordinate}}$$.
Common Questions
How do you find a rate from a coordinate graph?
Choose two points on the line, then calculate rise over run: (change in y) ÷ (change in x). This gives the rate of change or unit rate.
What do the y-axis and x-axis represent in a rate graph?
Typically, the y-axis shows the output quantity (distance, cost, etc.) and the x-axis shows the input (time, items, etc.). The ratio y/x is the rate.
How do you find the rate from points (2, 50) and (4, 100) on a distance-time graph?
Rate = (100 − 50) ÷ (4 − 2) = 50 ÷ 2 = 25. The rate is 25 miles per hour.
What does it mean when the graph is a straight line through the origin?
It indicates a proportional relationship with a constant unit rate. The rate equals the slope of the line: y/x for any point.
Can you find the rate from a table or equation as well as a graph?
Yes—from a table, divide any y-value by its x-value (for proportional tables). From an equation y = kx, k is the unit rate.
What is the difference between rate and unit rate on a coordinate graph?
The unit rate is the rate per 1 unit of x—it equals the y-value when x = 1. The slope of the line equals the unit rate for proportional relationships.