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Get familiar with gradients in this maths quiz.

Straight Line (F)

Learn GCSE straight-line graphs: use y = mx + c, find gradients and intercepts, test proportionality, and interpret lines in real contexts.

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Fascinating Fact:

In a recipe scale, a line through the origin means direct proportion. y = 0.75x passes through (0, 0), so doubling x doubles y.

In GCSE Maths, straight-line graphs model relationships using y = mx + c. You’ll calculate gradients, spot y-intercepts, decide if data are in direct proportion, and sketch or read lines to solve problems.

Key Terms

Gradient (m): The steepness of the line; change in y divided by change in x.
y-intercept (c): The value of y when x = 0; where the line crosses the y-axis.
Direct proportion: A relationship of the form y = kx that passes through the origin and scales linearly.

Frequently Asked Questions (Click to see answers)

How do I find the gradient from two points?

Use gradient = (y₂ − y₁) ÷ (x₂ − x₁). For points (1, 3) and (5, 11), gradient = (11 − 3) ÷ (5 − 1) = 8 ÷ 4 = 2.

What does y = mx + c tell me?

m is the gradient (steepness) and c is the y-intercept. Positive m slopes up; negative m slopes down. c shows where the line crosses the y-axis.

How can I tell if a graph shows direct proportion?

The line must be straight and pass through the origin (0, 0). Its equation has the form y = kx with no constant term; the gradient equals the constant of proportionality.