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Algebra · Foundation & Higher

Straight-line graphs (y = mx + c)

The equation y = mx + c describes a straight line. m is the gradient and c is the y-intercept.

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Key facts to remember

  • 1Gradient (m) = rise ÷ run = (change in y) ÷ (change in x).
  • 2The y-intercept (c) is where the line crosses the y-axis (x = 0).
  • 3Parallel lines have the same gradient.
  • 4Perpendicular lines have gradients that multiply to −1 (negative reciprocals).
  • 5To find the equation of a line: find m first, then substitute a point to find c.
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Formulas

Equation of a line
y = mx + c
Gradient
m = (y₂ − y₁) ÷ (x₂ − x₁)
Perpendicular gradient
m₂ = −1/m₁
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Worked examples

Example 1

Find the equation of the line through (2, 5) and (6, 13).

Working

  1. Gradient m = (13 − 5) ÷ (6 − 2) = 8 ÷ 4 = 2
  2. Use y = 2x + c with point (2, 5): 5 = 2(2) + c → c = 1
  3. Equation: y = 2x + 1
Answery = 2x + 1
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Common mistakes

✗Swapping the x and y coordinates when calculating gradient.
✗Reading the y-intercept as the x-intercept (where the line crosses the x-axis).
✗Confusing parallel (same m) with perpendicular (negative reciprocal m).
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Exam tips

✓When drawing a straight-line graph, plot at least 3 points to catch errors.
✓Rearrange equations like 2y = 4x + 6 → y = 2x + 3 before identifying m and c.

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