Straight-Line Graphs
Grade 4The equation of a straight line
Every straight line (that is not vertical) has the equation y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis).
To draw the line: plot the y-intercept at (0, c), then use the gradient to find a second point — go 1 across, m up — and draw through both.
Finding the gradient
Pick any two points on the line. Divide the vertical change by the horizontal change. A positive gradient goes up left-to-right; a negative gradient goes down.
Worked example — find the equation from two points
Parallel and perpendicular lines
Parallel lines have the same gradient. Perpendicular lines have gradients that multiply to −1 — so the perpendicular gradient is the negative reciprocal: if m = 3, the perpendicular gradient is −1/3.
Try this one
The diagram shows points \(R\) and \(S\) on a coordinate grid.
(a) Find the midpoint of \(RS\). [1]
(b) Find the equation of the line through \(R\) and \(S\). [3]
This question covers midpoints and linear graph equations.
Ask yourself: 'how do I find the midpoint of two points, and once I have the gradient, how do I use a point to find \(c\)?' For the midpoint, average the \(x\)-coordinates and average the \(y\)-coordinates separately.
