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Mathematics Essentials 11
Patterns and Relations
9. Solve problems involving relationships using graphing technology and pencil-and-paper techniques
9.8 Rate of change
Rate of Change
Rate of change measures how much y changes for every unit x changes, calculated as rise over run.
What You'll Learn
Rate of change = (change in y) / (change in x), or rise over run.
Given two points, subtract y-values and divide by the difference in x-values.
For a straight line, the rate of change is the same everywhere: the slope.
A steeper line has a larger rate of change.
Rate of change applies to real quantities like cost per minute or speed.
What You'll Practice
1
Graphing taxi fares with initial costs and per-kilometer rates
2
Calculating earnings based on base salary plus commission per item sold
3
Converting mixed time units to find speed in kilometers per hour
4
Determining cost per person by dividing total expenses among guests
Why This Matters
Rate of change appears everywhere in daily lifefrom calculating your paycheck to planning trip costs to understanding phone data plans. Mastering rates builds your problem-solving skills and prepares you for algebra, physics, and real-world financial decisions.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
Rate of Change
Unit Rate
Slope
Linear Graphs
Word Problems
Distance-Speed-Time
Unit Conversion
NS Curriculum Aligned