Every straight line (except vertical ones) can be written as y = mx + c. The number m is the gradient and c is the y-intercept, where the line crosses the y-axis. In y = 3x − 2, the gradient is 3 and the line crosses the y-axis at (0, −2).
To find the equation of a line through two points, first find the gradient m. Then put one point into y = mx + c to find c. Through (1, 3) and (4, 12): m = 9 ÷ 3 = 3, and 3 = 3 × 1 + c gives c = 0, so y = 3x.
Worked example
Find the equation of the line through (0, 5) and (2, 1).
- m = (1 − 5) ÷ (2 − 0) = −2.
- It crosses the y-axis at 5, so c = 5.
Answer:y = −2x + 5
Key words
- y-intercept
- where a line crosses the y-axis
- gradient (m)
- the steepness of the line
- linear
- making a straight line
Practise this
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Common Core-referenced: 8.F.B.4