First find the gradient: m = (y₂ − y₁)/(x₂ − x₁). Then substitute one point into y = mx + c to find c.
For (3, −18) and (5, −26): m = (−26 − (−18))/(5 − 3) = −8/2 = −4. Then −18 = −4 × 3 + c, so −18 = −12 + c and c = −6. The line is y = −4x − 6. Check with the second point: −4 × 5 − 6 = −26.
Worked example
Find the equation of the line through (2, −10) and (−1, 2).
- m = (2 − (−10))/(−1 − 2) = 12/−3 = −4.
- −10 = −4 × 2 + c, so c = −2.
Answer:y = −4x − 2
Key words
- gradient
- change in y ÷ change in x
- intercept
- where the line crosses the y-axis
- substitute
- put a point's values into the equation
Practise this
New questions every time.
Common Core-referenced: HSF-LE.A.2