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
A straight line passes through the point \((0, 4)\) and has gradient \(2\).
(a) Write down the equation of the line. [1]
(b) Another line is parallel to this line and passes through the point \((0, -1)\). Write down the equation of this second line. [1]
(c) Do the two lines ever meet? Give a reason for your answer. [1]
This question uses the straight-line equation \(y = mx + c\) and the idea of parallel lines.
Ask yourself: 'If two lines are parallel, what do they have in common — and what is different about them?' Remember that \(m\) is the gradient and \(c\) is where the line meets the y-axis.
