Straight-line graphs
Lesson 11 of 13
Gradient and intercept
Objective. Read the gradient and y-intercept from a straight-line graph.
The key idea
Gradient is rise over run: how much y changes for each 1 that x increases. The y-intercept is the value of y where the line crosses x = 0.
Worked example
A line passes through (0, 3) and (2, 7). Find its equation.
- 1Gradient: (7 − 3) ÷ (2 − 0) = 2.
- 2It crosses the y-axis at 3.
- 3So y = 2x + 3.
Answer: y = 2x + 3
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Calculating run over rise instead of rise over run.
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