The form y = mx + c
Objective. Read gradient and intercept directly from a linear equation.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
The equation y = mx + c describes a straight line, where m is the gradient (steepness) and c is the y-intercept, the point where the line crosses the y-axis. Once an equation is written in this exact form, the gradient and intercept can be read off directly without further calculation. For example, in y = 3x − 4, the gradient is 3 and the line crosses the y-axis at (0, −4). If an equation is not already in this form, such as 2y = 6x + 8, it must first be rearranged by dividing throughout by 2 to get y = 3x + 4 before the gradient and intercept can be identified.
Worked example
Write down the gradient and y-intercept of the line given by 4y = 8x − 12.
- 1Divide every term by 4 to isolate y: y = 2x − 3.
- 2The equation is now in the form y = mx + c.
- 3Compare to identify m: the gradient is 2.
- 4Compare to identify c: the y-intercept is −3.
Answer: Gradient = 2, y-intercept = −3
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Practice
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Start practisingCommon mistake. Pupils often read the gradient and intercept directly from an equation that has not yet been rearranged into y = mx + c form, such as reading a gradient of 6 from 2y = 6x + 8 instead of 3. Always isolate y with a coefficient of 1 before identifying m and c.
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