Equation of a Straight Line

Main form: y = mx + c

m = gradient, c = y-intercept (where line cuts y-axis)

Finding the equation

Method 1: If given gradient m and point (x₁, y₁):
y - y₁ = m(x - x₁)

Method 2: If given two points: first find m, then use Method 1.

Examples

Gradient 3, passes through (0, 2)   ⇒   y = 3x + 2

Through (1, 5) and (3, 9): m = (9-5)/(3-1) = 2, then y - 5 = 2(x - 1)   ⇒   y = 2x + 3

Other forms

Horizontal line: y = k

Vertical line: x = k

Discussion

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