What is important to know about Straight-line graphs (y = mx + c)?

Gradient (m) = rise ÷ run = (change in y) ÷ (change in x).

The y-intercept (c) is where the line crosses the y-axis (x = 0).

Parallel lines have the same gradient.

📐

Algebra · Foundation & Higher

Straight-line graphs (y = mx + c)

The equation y = mx + c describes a straight line. m is the gradient and c is the y-intercept.

🔑

1Gradient (m) = rise ÷ run = (change in y) ÷ (change in x).
2The y-intercept (c) is where the line crosses the y-axis (x = 0).
3Parallel lines have the same gradient.
4Perpendicular lines have gradients that multiply to −1 (negative reciprocals).
5To find the equation of a line: find m first, then substitute a point to find c.

📐

Equation of a line

y = mx + c

Gradient

m = (y₂ − y₁) ÷ (x₂ − x₁)

Perpendicular gradient

m₂ = −1/m₁

✍️

Example 1

Find the equation of the line through (2, 5) and (6, 13).

Working

Answery = 2x + 1

⚠️

✗Swapping the x and y coordinates when calculating gradient.

✗Reading the y-intercept as the x-intercept (where the line crosses the x-axis).

✗Confusing parallel (same m) with perpendicular (negative reciprocal m).

🎯

✓When drawing a straight-line graph, plot at least 3 points to catch errors.

✓Rearrange equations like 2y = 4x + 6 → y = 2x + 3 before identifying m and c.

Ready to test yourself on Straight-line graphs (y = mx + c)?

Get AI-marked practice questions on exactly this subtopic.

▶️ Watch on YouTube

Free video lessons

Click a topic to search

Opens YouTube — pick any free GCSE video.