Method 1: From a Graph
- Read the y-intercept c directly from the graph (where the line crosses the y-axis)
- Choose two clear points on the line (grid intersections)
- Calculate gradient: m = (change in y) ÷ (change in x)
- Write y = mx + c
Method 2: From Two Points
- Calculate gradient: m = (y₂ − y₁) ÷ (x₂ − x₁)
- Substitute m and one point into y = mx + c
- Solve for c
- Write the complete equation
Example: Find the equation of the line through (2, 7) and (5, 16).
Step 1: m = (16 − 7) ÷ (5 − 2) = 9 ÷ 3 = 3
Step 2: Substitute (2, 7): 7 = 3(2) + c → c = 7 − 6 = 1
Step 3: y = 3x + 1
Check with (5, 16): 3(5) + 1 = 16 ✓
This deep dive covers Finding the Equation of a Line within Linear Graphs Problems for GCSE Mathematics. Revise Linear Graphs Problems in Graphs for GCSE Mathematics with 16 exam-style questions and 11 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 3 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Linear Graphs Problems
A taxi company charges a fixed fee plus an amount per mile. On a cost graph (£ against miles), what does the y-intercept represent?
A plumber charges according to the formula C = 40t + 30, where C is the total cost in pounds and t is the time in hours. Explain what the values 40 and 30 represent in this context.