This topic summary covers Knowledge Organiser: Linear Graphs Problems 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 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Linear Graphs Problems
Key Formula
- y = mx + c
- m = (y₂ − y₁) ÷ (x₂ − x₁)
- Gradient = rate of change
- y-intercept = starting/fixed value
Finding the Equation
- From graph: read c, calculate m from two points
- From two points: calculate m first, then substitute to find c
- Always verify by checking both original points
- Simultaneous equations: find crossing point of two lines
Key Vocabulary
- Gradient: rate of change (rise ÷ run)
- y-intercept: starting value (fixed charge)
- Simultaneous: two equations solved at the same time
- Interpolation: predicting within the data range
- Extrapolation: predicting outside the data range
Common Errors
- Confusing y-intercept (crosses y-axis) with x-intercept
- Not including units with gradient in context questions
- Assuming extrapolation is reliable
- Not checking final equation against original points
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.