Equations of Straight Lines (y = mx + c) (WJEC GCSE Maths & Numeracy (Double Award): Foundation): Revision Note

Finding equations of straight lines

What is the equation of a straight line?

• The general equation of a straight line is y  = mx  + c  where

  • m  is the gradient

  • c  is the y-intercept

    • The value where it cuts the y-axis

• y  = 5x  + 2  is a straight line with

  • gradient 5

  • y-intercept 2

• y  = 3 - 4x  is a straight line with

  • gradient -4

  • y-intercept 3

How do I find the equation of a straight line from a graph?

• Find the gradient by drawing a triangle and using

  • $\mathrm{gradient}=\frac{\mathrm{rise}}{\mathrm{run}}$

    • Positive for uphill lines, negative for downhill

• Read off the y-intercept from the graph

  • Where it cuts the y-axis

• Substitute these values into y  = mx  + c 

What if no y-intercept is shown?

• If you can't read off the y-intercept

  • find any point on the line

  • substitute it into the equation

  • solve to find c 

• For example, a line with gradient 6 passes through (2, 15)

  • The y-intercept is unknown

    • Write y  = 6x  + c

  • Substitute in x  = 2 and y  = 15

    • 15 = 6 × 2 + c

    • 15 = 12 + c

  • Solve for c

    • c  = 3

  • The equation is y  = 6x  + 3

What are the equations of horizontal and vertical lines?

• A horizontal line has the equation y  = c

  • c  is the y-intercept

• A vertical line has the equation x  = k

  •  k  is the x-intercept

• For example

  • y = 4

  • x = -2