Comparing Linear Functions: Rate of Change
This Grade 8 math skill from Pengi Math (Grade 8) teaches students to compare linear functions by analyzing their rates of change (slopes). Students determine which function grows faster by comparing slopes given in different forms—equations, graphs, tables, or verbal descriptions—and interpret what a greater rate of change means in context.
Key Concepts
When comparing linear functions, the slope determines the rate of change and direction. Functions with positive slopes increase as $x$ increases, while functions with negative slopes decrease as $x$ increases. The absolute value of the slope indicates how quickly the function values change.
Common Questions
How do you compare the rate of change of two linear functions?
Find the slope of each function (from its equation, graph, or table), then compare the values. A steeper slope means a greater rate of change.
What is the rate of change of a linear function?
The rate of change is the slope, which tells you how much the output (y) changes for each unit increase in the input (x).
How do you find slope from a table of values?
Choose any two rows, compute (change in y) / (change in x) = (y2 - y1) / (x2 - x1). This gives the slope.
Why is comparing rates of change important?
Comparing slopes helps you determine which situation is growing faster, which is key in real-world contexts like speed, pricing, and population growth.
Where is comparing linear functions by rate of change taught?
This skill is covered in the Grade 8 Pengi Math textbook under linear functions and slope.