y = mx + c

m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis).

Formula: y = mx + c

Example: y = 3x + 2 Gradient = 3, y-intercept = 2

Finding the Gradient

Gradient = rise ÷ run = change in y ÷ change in x.

Formula: m = (y₂ − y₁) / (x₂ − x₁)

Example: Points (1, 3) and (3, 7): m = (7−3)/(3−1) = 4/2 = 2

Drawing from a Table

Substitute x values into the equation to find y values, then plot the points.

x = a and y = b

x = a is a VERTICAL line through a. y = b is a HORIZONTAL line through b.

Example: x = 3 is a vertical line.

Intercepts

x-intercept is where y=0. y-intercept is where x=0.

Finding the Equation

If you know the gradient and a point, substitute into y = mx + c to find c.

Example: Gradient 2, passes through (3, 8): 8 = 2(3) + c c = 2 y = 2x + 2

Parallel Lines

Lines are parallel if they have the SAME gradient.

Example: y = 2x + 5 and y = 2x - 3 are parallel.

Perpendicular Lines

Parallel lines have gradients that multiply to −1. (Negative reciprocal).

Formula: m₁ × m₂ = −1

Example: Line: y = 3x + 1 Perpendicular: m = −1/3

Real World Graphs

The gradient represents the rate of change (e.g. speed on a distance-time graph).

Midpoints & Lengths

Find the midpoint between two points by averaging the x and y coordinates.

Formula: Midpoint = [(x1+x2)/2 , (y1+y2)/2]