Coordinates and straight-line graphs
Plotting points, gradients and y = mx + c
Coordinates tell you exactly where a point is. Straight-line graphs show how two things are linked.
Coordinates and lines
- A coordinate (x, y): go along the x-axis first, then up or down the y-axis. “Along the corridor, then up the stairs.”
- The midpoint of (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2).
- A straight line has the equation y = mx + c: m is the gradient (steepness), c is where it crosses the y-axis.
- Gradient = change in y ÷ change in x.
Worked examples
Example 1. Find the midpoint of (2, 3) and (8, 7).
Example 2. For y = 3x − 2, find y when x = 4.
Example 3. Find the gradient of the line through (1, 2) and (3, 8).
Example 4. What are the gradient and y-intercept of y = −2x + 5?
Top tips and common mistakes
- Make a table of values (x = −2 to 3) before drawing a line.
- Horizontal lines are y = a number; vertical lines are x = a number.
- Parallel lines have the same gradient.
My favourite trick: “along the corridor, then up the stairs” for coordinates!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Coordinates and straight-line graphs worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.