y = mx + c
Practise y = mx + c with this free Foundation GCSE Maths worksheet from Virtus Academy. You'll work through using y = mx + c to find the equation of a line, building confidence for your exam, and every question comes with worked solutions in the mark scheme. Suitable for AQA, Edexcel and OCR. The gradient m gives the steepness; c is where the line crosses the y-axis.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
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Topic overview
The equation \(y = mx + c\) describes any straight line. The letter \(m\) is the gradient and \(c\) is the \(y\)-intercept, the point where the line crosses the \(y\)-axis.
Reading a line's equation therefore tells you everything about it without plotting anything. In \(y = 3x - 2\), the gradient is \(3\) and the line crosses the \(y\)-axis at \(-2\).
The form only works when \(y\) is on its own. An equation such as \(2y = 6x + 4\) must be divided through by \(2\) first, giving \(y = 3x + 2\). Reading the gradient as \(6\) from the original is a very common error.
Revision notes
Reading gradient and intercept
Once the equation is in the form \(y = mx + c\), the number in front of \(x\) is the gradient and the constant is the intercept.
In \(y = -4x + 7\), the gradient is \(-4\) and the line crosses the \(y\)-axis at \((0, 7)\).
Rearranging into the right form
If \(y\) is not alone, rearrange first. Divide everything by the coefficient of \(y\), or move terms across.
From \(3y - 6x = 9\): add \(6x\) to get \(3y = 6x + 9\), then divide by \(3\) to get \(y = 2x + 3\).
Writing an equation from a graph
Find the gradient from two points and read the intercept where the line crosses the \(y\)-axis, then substitute both into the form.
A line with gradient \(2\) crossing at \(-1\) has equation \(y = 2x - 1\).
Key points
- \(y = mx + c\) describes a straight line.
- \(m\) is the gradient.
- \(c\) is the y-intercept.
- \(y\) must be on its own before reading \(m\) and \(c\).
- A negative \(m\) means the line slopes downwards.
- The line crosses the y-axis at \((0, c)\).
Worked examples
Example 1
Write down the gradient and y-intercept of \(y = 5x - 3\).
Working
Example 2
Find the gradient of \(2y = 8x + 6\).
Working
Example 3
A line has gradient \(-3\) and crosses the y-axis at \(4\). Write its equation.
Working
Common mistakes
Reading the gradient before rearranging.
In 2y = 8x + 6 the gradient is 4, not 8. Divide through so y is alone first.
Mixing up m and c.
The gradient multiplies x; the intercept stands alone.
Losing the sign of the intercept.
In y = 3x − 2 the intercept is −2, not 2.
Assuming a steeper-looking line has a larger gradient.
The scales on the axes may differ, so calculate rather than eyeball.
Exam tips
- Always rearrange to y = mx + c before reading anything off.
- State the gradient and intercept separately with their signs.
- Check the intercept against where the line meets the y-axis.
- Use two clear points to verify a gradient you have read.
Key terms
- Gradient
- The steepness of a line, given by \(m\).
- y-intercept
- Where the line crosses the y-axis, given by \(c\).
- Coefficient
- The number multiplying a variable.
- Rearrange
- To rewrite an equation with a chosen variable on its own.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.