IGCSE Maths / Graphs of straight lines
y = mx + c and the shape of the line
Edexcel International GCSE Maths (4MA1), chapter 6: Graphs of straight lines, specification point 3.3h-f. Free lesson.
Read the revision notes · IGCSE Maths past papers
The form y = mx + c describes a straight line: m gives its gradient and c gives where it crosses the vertical axis. Put the equation into this form before reading off either value.
What m and c tell you
In y = mx + c, the two letters describe the line. The gradient m tells you how much the line rises or falls for each step of one across. The vertical intercept c is the y-value where the line crosses the vertical axis. A positive gradient means the line leans uphill. A negative gradient means it leans downhill. The sign tells you the direction, while the size of the gradient tells you how steep the line is.
How to read the gradient and intercept
Read m and c only when the equation is written with y on its own. For example, in y = 4x − 3, the coefficient of x is 4 and the number on its own is −3. m = 4, so the line rises 4 for each 1 across. c = −3, so the line crosses the vertical axis at −3.
How to rearrange before reading m
If there is a number in front of y, divide every term by that number. This leaves y on its own, so the coefficient of x becomes the true gradient. For 2y = 6x + 10, the 6 is not the gradient yet because y does not stand alone. Dividing every term by 2 gives y = 3x + 5, so the gradient is 3.
How m and c appear on a graph
A line through (0, 1) and (3, 7) rises 6 while moving 3 across. Its gradient is 6 ÷ 3 = 2. Substituting (3, 7) into y = 2x + c gives 7 = 2 × 3 + c, so c = 1. The equation is y = 2x + 1. The gradient triangle shows the change up and across. Here, 6 up and 3 across gives m = 2. The point (0, 1) lies on the vertical axis, so the line crosses at c = 1.
How to compare positive and negative gradients
A gradient of −5 is not shallower than a gradient of 2. The minus sign shows that the line falls. Compare steepness using the size of the gradient, ignoring its sign. Gradient −5 changes 5 units vertically for each 1 across, so it is steeper than gradient 2. Gradient 2 rises, while gradient −5 falls.
A quick rearranging check
For 3y = 12x − 6, divide every term by 3 before reading the values. This gives y = 4x − 2, so the gradient is 4 and the vertical intercept is −2. A negative gradient means downhill, not necessarily shallow. The gradient and intercept describe the line, so they let you identify its shape and crossing without making a table.