Parallel linear graphs
Objective. Recognise that parallel lines have equal gradients.
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- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Parallel lines never meet because they rise and fall at exactly the same rate, meaning their equations in the form y = mx + c share an identical gradient m, even though their intercepts c can differ. To check whether two lines are parallel, rearrange both into y = mx + c form and compare the coefficients of x. For example, y = 2x + 5 and y = 2x − 3 are parallel because both have gradient 2, despite crossing the y-axis at different points. To find the equation of a line parallel to a given one through a new point, keep the same gradient and use the new point to calculate a fresh value of c.
Worked example
A line is parallel to y = 3x + 2 and passes through the point (0, 7). Find the equation of this parallel line.
- 1Parallel lines share the same gradient, so the new line has gradient 3.
- 2The line passes through (0, 7), so this point is the y-intercept.
- 3Therefore c = 7.
- 4Write the equation using m = 3 and c = 7: y = 3x + 7.
Answer: y = 3x + 7
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Practice
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Start practisingCommon mistake. Pupils sometimes assume lines with the same y-intercept are parallel rather than checking the gradients, confusing c with m. Always compare the coefficients of x, not the constant terms, to test for parallel lines.
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