Use two points
Find the line through (1, 2) and (3, 6).
- Gradient = (6 − 2)/(3 − 1) = 2.
- Use y − 2 = 2(x − 1).
Answer: y = 2x
Equations of straight lines
Find gradients and recognise equivalent equations of a line.
Before you start
You’ll need Three simultaneous linear equations. Follow a link if you want to revise it first.
Gradient and a point
Gradient measures change in y divided by change in x. A vertical line has no finite gradient.
With point (x₀, y₀) and gradient m, use y − y₀ = m(x − x₀). Expand only after the point is substituted.
Multiplying every term of a line equation by the same nonzero number gives an equivalent equation.
Parallel lines share a gradient; identical lines must also pass through the same point.
Writing the same line in different forms
Recognise an equivalent equation
Explain why 4x − 2y = 0 describes the same line.
- Divide every term by the nonzero number 2.
- This gives 2x − y = 0, or y = 2x.
Answer: The equations are equivalent.
Keep the order of the points the same in numerator and denominator.
Practice questions
The first link uses smaller values. Move on when you can answer without referring to the examples. The difficulty settings aren’t tied to exam grades.
Practice is filtered to your selected course. Change course or options when needed.
Check your understanding
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Why does the two-point gradient formula fail for a vertical line?