0580

Linear Graphs

Coordinate Geometry and Graphs

From a graph

A downhill line crossing the y-axis at 5 and the x-axis at 10, with a red right-angled triangle marking 4 down against 8 across between (2, 4) and (10, 0), so the gradient is −0.5
Source: Finding equations of straight lines by Save My Exams
  • Work out the gradient from a triangle, then read where the line crosses the y-axis
  • Put both numbers into y = mx + c and write the equation out
  • If the crossing point is off the edge of the grid, use a point the line does pass through instead

From a gradient and a point

  • Write y = mx + c with the gradient filled in and c left as a letter
  • Substitute the coordinates of the known point and solve the resulting equation for c
  • Rewrite the equation with that value in place
Worked example

A gradient and one point

Find the equation of the line with gradient 5 that passes through (3, 7). Give your answer in the form y = mx + c.

Solution:

  • Start from y = 5x + c
  • Substitute x = 3 and y = 7: 7 = 5 × 3 + c
  • So 7 = 15 + c
  • Subtract 15: c = −8
  • The equation is y = 5x − 8