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MathidiaMathematics Academy
Graphs and functions
Lesson 33 of 75
Standard practice

Find a line equation

Objective. Determine a line from its gradient and intercept.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Finding a line's equation means determining the values of m and c so the full equation y = mx + c can be written. If the gradient and a point on the line are known, substitute both into y = mx + c and solve for c. For example, a line with gradient 4 passing through (2, 9) gives 9 = 4(2) + c, so 9 = 8 + c, meaning c = 1, and the full equation is y = 4x + 1. If two points are given instead, first calculate the gradient using (change in y) ÷ (change in x), then proceed as before to find c.

Worked example

A straight line has gradient 5 and passes through the point (3, 19). Find the equation of the line.

5 … 3
Coordinate grid with the line 5 … 3
  1. 1Start with the general form y = mx + c, using m = 5.
  2. 2Substitute the point (3, 19): 19 = 5(3) + c.
  3. 3Calculate: 19 = 15 + c.
  4. 4Subtract 15 from both sides: c = 4, so the equation is y = 5x + 4.

Answer: y = 5x + 4

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Common mistake. Pupils sometimes substitute the x and y coordinates of the given point into the wrong positions, swapping which value goes where in y = mx + c. Always substitute the y-coordinate for y and the x-coordinate for x precisely.

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