FUN006 · Functions & graphs · Classes 9–11
Linear function
A linear function f(x) = mx + c changes by the same amount m for each step of 1 in x. Its graph is a straight line with slope m and y-intercept c.
y = mx + cLinear function
📐 Formula
f(x) = mx + c; slope m = Δy/Δx
✏️ Worked example
f(x) = 2x + 1: slope 2, y-intercept 1, x-intercept −0.5.
🌍 Where it is used
Fixed rates: phone plans, taxi fares, converting units.
❓ Quick check
Slope of f(x) = −3x + 7?
🏋️ Practice
Easyf(x) = 4x − 2. f(3) = ?
Answer: 10
MediumLine through (0, 1) with slope 3?
Answer: f(x) = 3x + 1
ChallengeLinear function with f(0) = 5, f(2) = 9?
Answer: f(x) = 2x + 5