Knowledge Organiser: Straight Line Graphs
Part of Straight Line Graphs · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Straight Line Graphs within Straight Line Graphs for GCSE Mathematics. Revise Straight Line Graphs in Graphs for GCSE Mathematics with 14 exam-style questions and 20 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 8
Practice
14 questions
Recall
20 flashcards
Knowledge Organiser: Straight Line Graphs
Key Terms
- Linear graph: A straight-line graph showing a constant rate of change
- Gradient (m): The steepness of the line — rise divided by run
- y-intercept (c): Where the line crosses the y-axis (when x = 0)
- x-intercept: Where the line crosses the x-axis (when y = 0)
- Table of values: A list of (x, y) pairs used to plot a graph
- y = mx + c: The standard form of a straight-line equation
Must-Know Facts
- A positive gradient (m > 0) slopes upward from left to right
- A negative gradient (m < 0) slopes downward from left to right
- y = c is a horizontal line with gradient zero
- x = k is a vertical line with an undefined gradient
- To draw a line: plot at least 3 points from a table of values, then use a ruler
- To find the equation from a graph: read c from the y-axis, then calculate m using two points
Key Formulas
- Equation of a straight line: y = mx + c
- Gradient = (y₂ − y₁) ÷ (x₂ − x₁) = rise ÷ run
- y-intercept: substitute x = 0 into the equation
- x-intercept: set y = 0 and solve for x
Common Mistakes
- Negative gradient direction: A negative gradient means the line goes down from left to right — don't confuse with a positive gradient
- Gradient calculation: Use rise ÷ run — don't accidentally do run ÷ rise
- c is the y-intercept not the x-intercept: The line crosses the y-axis at (0, c), not (c, 0)
- Plotting from table of values: Use at least 3 points and check they are collinear before drawing the line
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Practice Questions for Straight Line Graphs
A straight line has the equation y = 3x + 7. What is the gradient of this line?
Line A has equation y = 3x + 1. Line B has equation y = 3x - 5. Explain why lines A and B are parallel. Include the values of their gradients in your answer.
Quick Recall Flashcards
14 questions on Straight Line Graphs — practise free
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