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Grade 8 Math Lab: Functions & Proofs FREE
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Comparing Linear Functions
Learning Objectives
- Compare rates of change
- Analyze functions in different representations
- Determine faster/slower rates
Key Concepts
Rate of Change
Slope — how fast the output changes per unit input
Initial Value
The y-intercept or starting point
Theory
**Comparing linear functions** across tables, graphs, and equations:
- Greater slope = steeper line = faster rate
- Compare y-intercepts for starting values
**From a table:** slope = Δy/Δx between consecutive rows
**From a graph:** slope = rise/run
**From an equation:** y = mx + b → slope is m
Examples
f(x) = 2x + 5 vs g(x) = 4x + 1. Which grows faster?
Solution: g(x) — slope 4 > slope 2