Coordinate geometry and vectorsAdditional / Further Maths

Equation of a line from a point and gradient

Use the gradient and one point to find line’s equation.

  • Use , or substitute the point into .
  • Expand and rearrange if an equation in gradient-intercept form is wanted.

Example 1

Use point-gradient form

Find the equation of the line. Gradient , through .

Expand the brackets and collect like terms.Apply this to both sides.

Example 2

Determine the equation of the required line. Gradient , through .

Expand the brackets and collect like terms.Apply this to both sides.

Your turn

Question 1

Find the equation of the line through with gradient .

Check answer
Apply this to both sides.
Question 2

Find the equation of the line through with gradient .

Check answer
Apply this to both sides.
Question 3

Find the equation of the line through with gradient .

Check answer
Apply this to both sides.
Question 4

Find the equation of the line through with gradient .

Check answer
Apply this to both sides.
Question 5

Find the equation of the line through with gradient .

Check answer
Apply this to both sides.
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