Curriculum fit: GCSE Maths Algebra (Foundation and Higher). US: Grade 8 and Algebra I linear functions (Common Core Functions).
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What Is It?
A straight line graph shows a linear relationship between x and y. Its equation can be written as y = mx + c, where m is the gradient (how steep the line is) and c is the y-intercept (where the line crosses the y-axis).
A positive gradient slopes up from left to right. A negative gradient slopes down. A gradient of zero is a horizontal line.
Key Formulas and Ideas
- y = mx + c: m is the gradient, c is the y-intercept.
- Gradient = change in y ÷ change in x = (y₂ − y₁) ÷ (x₂ − x₁).
- Parallel lines have the same gradient.
Worked Examples
Reading m and c
State the gradient and y-intercept of y = −½x + 4.
- Compare with y = mx + c.
- m = −½ and c = 4.
✓ Answer Gradient −½, y-intercept 4
Gradient From Two Points
Find the gradient of the line through (1, 2) and (3, 8).
- Change in y: 8 − 2 = 6.
- Change in x: 3 − 1 = 2.
- Gradient = 6 ÷ 2 = 3.
✓ Answer 3
Plotting a Line
Draw y = 2x − 3 for x from 0 to 3.
- Work out y for each x: x = 0 gives −3, x = 1 gives −1, x = 2 gives 1, x = 3 gives 3.
- Plot (0, −3), (1, −1), (2, 1), (3, 3) and join them with a ruler.
✓ Answer A straight line through those four points
Common Mistakes to Avoid
- Calculating gradient as change in x ÷ change in y.
- Subtracting the coordinates in different orders on top and bottom.
- Confusing the y-intercept with the x-intercept.
- Not rearranging first: 2y = 4x + 6 has gradient 2, not 4.
Practice Questions
Frequently Asked Questions
What does a gradient of 3 mean?
For every 1 unit across, the line goes up 3 units.
How do I find where a line crosses the x-axis?
Set y = 0 and solve for x.
Keep Going With These Guides
Find the Equation of a Line From Two Points
Work out the gradient (slope), find the y-intercept and write the equation of a line, plus parallel and perpendicular lines and midpoints.
GCSEA-LevelHigh SchoolSimultaneous Equations (Systems of Equations) Step by Step
Solve two equations with two unknowns using elimination and substitution. Worked examples for GCSE simultaneous equations and Algebra 1 systems.
GCSEHigh SchoolSolving Inequalities and Showing Them on a Number Line
Solve linear inequalities, including double inequalities, and remember to reverse the sign when dividing by a negative, with worked examples.
GCSEHigh SchoolSources and Review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.