In short: To draw a straight line graph from an equation, read the y-intercept c (where the line crosses the y-axis) and the gradient m from y = mx + c. Plot the intercept, use the gradient to find a second point, then join them with a straight line. A small table of values is the most reliable method in an exam.
Drawing a straight line graph from an equation is a guaranteed source of marks on the GCSE Higher maths paper (AQA), and it underpins simultaneous equations, inequalities and real-life graphs. This guide gives you a method that never fails — a table of values — plus the faster gradient-and-intercept shortcut, a worked example, and the slips that lose marks.
The reliable method
The safest approach in an exam is a table of values. Here is the full procedure for an equation written as y = mx + c.
- Identify m and c. In y = mx + c, m is the gradient and c is the y-intercept. Make sure the equation is in this form first.
- Choose three x-values. Pick three convenient values that fit your axes, such as x = 0, 1 and 2. Three points let you spot any error — they must line up.
- Work out each y-value. Substitute each x into the equation and record the result in a table.
- Plot the points. Mark each (x, y) pair on the grid carefully.
- Join with a straight line. Use a ruler to draw a single straight line through all three points and extend it across the grid. Label it with its equation.
If the three points do not form a straight line, recheck your arithmetic before drawing.
A worked example
Draw the graph of y = 2x + 1 for values of x from −1 to 2.
Step 1 — identify m and c. Here m = 2 (gradient) and c = 1 (the line crosses the y-axis at 1).
Step 2 and 3 — build a table of values. Substitute each x into y = 2x + 1:
| x | −1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y | −1 | 1 | 3 | 5 |
Working: 2 × (−1) + 1 = −1; 2 × 0 + 1 = 1; 2 × 1 + 1 = 3; 2 × 2 + 1 = 5.
Step 4 — plot the points. Mark (−1, −1), (0, 1), (1, 3) and (2, 5) on the grid.
Step 5 — join them. A ruled line through these points crosses the y-axis at 1 and climbs 2 units for every 1 unit across, matching m = 2 and c = 1.
This works because every (x, y) pair you calculate is a point that obeys the equation, so they all sit on the same straight line. The intercept fixes where the line starts and the gradient fixes how steeply it rises.
Common mistakes to avoid
- Plotting before rearranging. If the equation is not yet in the form y = mx + c, reading the gradient straight off can go wrong. Rearrange first, then plot — confusing the roles of m and c is the classic [slope-intercept reversal](/misconceptions/slope-intercept-reversal).
- Using only two points. Two points always look like a straight line even if one is wrong. A third point reveals the error.
- Misreading the scale. Check how many small squares make one unit on each axis before plotting. A 2-units-per-square scale catches many students out.
- Freehand lines. Always use a ruler. A wobbly line can miss the printed points and lose accuracy marks.
- Arithmetic slips with negatives. For x = −1, compute 2 × (−1) + 1 = −1, not 2 × (−1) + 1 = 3. Use brackets to keep the sign right.
Frequently asked questions
How do you plot a straight line graph using y = mx + c? Read off c (the y-intercept) and m (the gradient). Plot the point (0, c), then use the gradient to step to more points, or build a table of values by substituting several x-values into the equation. Join the points with a ruled straight line.
How many points do you need to draw a straight line? Two points define a straight line, but plot at least three. The third acts as a check — if all three line up, your arithmetic is correct.
What do m and c mean in y = mx + c? m is the gradient, which controls the steepness and direction of the line. c is the y-intercept, the value of y where the line crosses the y-axis (when x = 0).
How do you draw a line if the equation is not in y = mx + c form? Rearrange it into y = mx + c first by isolating y. For example, 2y = 4x + 6 becomes y = 2x + 3. Then build a table of values or use the gradient and intercept.
What does a steeper line tell you about the equation? A steeper line has a larger gradient m. A line with gradient 3 rises faster than one with gradient 1. A negative gradient slopes downwards from left to right.
Practise this
See which slips cost you marks — [take the free diagnostic](/diagnostic). Related: [slope-intercept reversal explained](/misconceptions/slope-intercept-reversal).