y = mx + c (straight-line graphs)
m is the gradient (slope), c is the y-intercept (where the line crosses the y-axis).
Every straight line (except vertical) can be written y = mx + c. Find m by ‘rise over run’ between any two points; find c by reading off where the line crosses the y-axis.
Worked examples
y = 2x + 3: gradient 2, y-intercept 3.
Through (1, 5) and (3, 9): m = (9−5)/(3−1) = 2. Then c = 5 − 2×1 = 3.
Parallel lines have the same gradient. y = 2x + 3 and y = 2x − 1 are parallel.
Frequently asked questions
Negative gradient?
Line slopes downwards from left to right. y = −3x + 4 starts at (0, 4) and falls.
What if the line is vertical?
x = 4 (independent of y). Cannot be written y = mx + c — the gradient is undefined.