Straight-Line Graphs

Straight-line graphs represent linear relationships between two variables. Understanding the equation of a straight line, its gradient, and its intercept is fundamental to AQA GCSE Mathematics. This topic connects algebra with geometry and appears on both Foundation and Higher tier papers.

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The Equation y = mx + c

Every straight line can be written in the form:

y = mx + c

where:

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

Feature	Meaning	Example in y = 3x - 2
m (gradient)	How steep the line is; rise over run	m = 3 (goes up 3 for every 1 across)
c (y-intercept)	Where the line crosses the y-axis	c = -2 (crosses at (0, -2))

Exam Tip: If a line equation is written as y = c + mx (the terms swapped), it is still in the same form. The coefficient of x is always the gradient and the constant term is always the y-intercept.

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Gradient