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y = mx +c

Maths: Edexcel A Level Pure Maths, topic 3.1.1

Straight Line Graphs

Any straight line can be written as y = mx + c.

y mx + c

y = mx + c

  • m is the gradient of the line
  • c is the y-intercept (the height of the point where the line crosses the y axis).
Parallel lines have the same gradient

Parallel lines have the same gradient

  • y = 3x + 2 and y = 3x - 4 are parallel lines because they have the same gradient (3).
Perpendicular lines cross at a right angle

Perpendicular lines cross at a right angle

  • This happens when the two gradients multiply to give -1:
  • y = 2x + 4
  • y = -1⁄2x - 5
  • These are perpendicular lines because 2 × (-1⁄2) = -1.

Test yourself on y = mx +c

  • Show that the lines y = -2x + 2 and y = 1⁄2x + 4 are perpendicular.

  • Show that the lines y = 7x + 5 and y = -1⁄7x - 3 are perpendicular.

  • Show that the lines y = 7x + 5 and y = 7x - 3 are parallel.

  • Show that the lines y = -2x + 1 and y = -2x + 3 are parallel.

  • Are the lines y = 3.5x - 17 and y = 3.5x -1.5 parallel, vertical or perpendicular?

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