Equations of straight lines

Revise Equations of straight lines for Mathematics D 4024 (O Level) — revision notes, 8 practice questions and instant AI marking.

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Cambridge O Level Mathematics (Syllabus D) 4024

Equations of straight lines

The big idea: Every non-vertical straight line can be written y = mx + c: m is the gradient and c is where it crosses the y-axis. To find an equation, find m, then use a point on the line to find c.

Summary — What This Chapter Covers

Interpret and obtain the equation of a straight-line graph in the forms y = mx + c, ax + by = c and x = k.
Find the gradient and y-intercept from an equation such as 5x + 4y = 8.
Find the equation of a line from its graph or from two points.
Give equations in fully simplified form.

1. Reading y = mx + c

Syllabus 3.5 · Paper 1 & 2

Gradient m, y-intercept c

In y = mx + c, the coefficient of x is the gradient and the constant is the y-intercept: the line crosses the y-axis at (0, c). If the equation is in another form, rearrange it to make y the subject first.

Worked Example

Find the gradient and the y-intercept of the graph with equation 5x + 4y = 8.

Practice Question 1

Write down the gradient and y-intercept of (a) y = 7 − 4x (b) 2y = 3x + 1 (c) x = 5

2. Finding the Equation of a Line

Syllabus 3.5 · Paper 1 & 2

Gradient first, then substitute a point

From a graph: read the y-intercept c, and find the gradient m using two points on the line. From two points: find m, substitute one point into y = mx + c and solve for c. Check with the other point.

Worked Example

Find the equation of the straight line through (−1, 4) and (3, −8).

Practice Question 2

A straight line crosses the y-axis at (0, −4) and passes through (6, 0). Find its equation. Give your answer in the form ax + by = c, where a, b and c are integers.

3. Where Two Lines Meet

Syllabus 3.5 · Paper 1 & 2

Solve the equations simultaneously

The point where two lines cross lies on both, so its coordinates satisfy both equations. Solve them simultaneously (substitution is quick when one equation is y = …).

Practice Question 3

Memorise

y = mx + c

m = gradient, c = y-intercept.

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Equations of straight lines