Straight lines and gradients
Use a gradient and one known point to determine a nonvertical line.
Read the lesson: Equations of straight lines
The gradient through two distinct points is change in y divided by change in x. If the change in x is zero, the line is vertical and has equation x = constant; the gradient is undefined.
Parallel nonvertical lines have equal gradients. Perpendicular nonvertical lines have gradient product −1. A horizontal line and a vertical line are also perpendicular, so treat that case without dividing by zero.
Worked example
Find the line through (2,5) perpendicular to y = 2x − 3.
- The given gradient is 2, so the perpendicular gradient is −1/2.
- Use y − 5 = −(x − 2)/2.
- Rearrange or leave in point-gradient form.
Answer: y = −x/2 + 6
Practise straight lines and gradients
Course mapping
These specification references show where the topic occurs. The questions cover only some parts of each topic.
- 8365 · core · 3.5: Straight line equations
- 7M20 · core · A2.4: Straight line equations
- 6993 · core · CG1–CG5: Straight line equations
- 4PM1 · core · 8C–8E: Straight line equations
- 8365 · core · 3.5: A line through two points
- 7M20 · core · A2.4: A line through two points
- 6993 · core · CG1–CG5: A line through two points
- 4PM1 · core · 8C–8E: A line through two points
- 8365 · core · 3.5: Equivalent equations including horizontal and vertical lines
- 7M20 · core · A2.4: Equivalent equations including horizontal and vertical lines
- 6993 · core · CG1–CG5: Equivalent equations including horizontal and vertical lines
- 4PM1 · core · 8C–8E: Equivalent equations including horizontal and vertical lines
Next practice: Circles and tangents, Tangents and normals.