Mathematics 0580 Chapter Notes
What this chapter covers
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A straight line with equation y = mx + c has gradient m and crosses the y-axis at c. Parallel lines have equal gradients.
The gradient of y = 4x - 1 is 4. Every line parallel to it has the form y = 4x + c. Only c changes.
Worked example 12 marks
Line L has equation y = 3x - 7. Write down the equation of a line parallel to L that crosses the y-axis at (0, 4).
parallel lines have the same gradient, so m = 3 [1]
c = 4, so y = 3x + 4 [1]
Keep the same gradient. Write y = mx + c with that value of m.
Substitute the x and y of the given point and solve for c. Then write the full equation with the gradient and c in place.
Examiner insight
Worked example 12 marks
Find the equation of the line parallel to y = 4x + 3 that passes through (2, 9).
parallel, so the gradient is 4 and y = 4x + c [1]
9 = 4 × 2 + c, so c = 1 and y = 4x + 1 [1]
A negative gradient stays negative. Parallel lines have equal gradients, so do not change the sign. Take care with signs when you substitute: a positive x with a negative gradient gives a negative product.
An equation needs y = at the start and the x inside it.
Examiner insight
Worked example 12 marks
Find the equation of the line parallel to y = -2x + 5 that passes through (3, 4).
parallel, so the gradient is -2 and y = -2x + c [1]
4 = -2 × 3 + c, so 4 = -6 + c, c = 10 and y = -2x + 10 [1]
Recap
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