Line Graph Practice
Line graph questions ask you to compare line segments on a coordinate grid. The key is to calculate gradients carefully, then use the rules for parallel lines, perpendicular lines, translations, and missing coordinates.
The Rules Every Line Graph Question Uses
The papers focus on coordinate line segments: finding gradients, comparing parallel lines, checking perpendicular lines, translating a line, and using a known gradient to find a missing coordinate.
📈 Rule 1: Gradient is rise over run
Subtract the y-values, then divide by the change in x-values.
Example: From (3, 4) to (6, 2), gradient = 2 - 46 - 3 = -23.
∥ Rule 2: Parallel lines have the same gradient
If two line segments have equal gradients, they are parallel.
Example: A line with gradient -12 is parallel to any other line with gradient -12.
⊥ Rule 3: Perpendicular gradients multiply to -1
For a perpendicular line, flip the fraction and change the sign.
Example: A line with gradient -1 has perpendicular gradient 1.
↔ Rule 4: Translations move both endpoints
Apply the same change to both coordinates of both endpoints.
Example: Moving (5, 1) and (7, 2) two left and one up gives (3, 2) and (5, 3).
How to Solve Line Graph Questions
Three useful moves: calculate the gradient, compare it with each option, and watch for translations or missing coordinate traps.
1. Find a Parallel Line
Question: Which line is parallel to the line from (3, 4) to (6, 2)?
Worked Method
Step 1: Gradient = 2 - 46 - 3 = -23.
Step 2: A parallel line must also have gradient -23.
Tip: Check each option by calculating its gradient, not by judging the drawing by eye.
2. Translate Both Endpoints
Question: Which option shows the same line from (5, 1) to (7, 2) moved 2 squares left and 1 square up?
Worked Method
Step 1: A move 2 left and 1 up means x - 2 and y + 1.
Step 2: (5, 1) becomes (3, 2).
Step 3: (7, 2) becomes (5, 3).
Tip: Translate both endpoints. Moving only one endpoint changes the gradient.
3. Use the Parallel Gradient to Find a Missing Coordinate
Question: A second line joins (2, 5) to (6, y). If it is parallel to a line from (3, 1) to (7, 2), what is y?
Worked Method
Step 1: Gradient of the first line = 2 - 17 - 3 = 14.
Step 2: The second line must also have gradient 14.
Step 3: Its run is 6 - 2 = 4, so the rise must be 1.
Tip: y = 5 + 1 = 6.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Line Graphs pack contains 90 questions across 3 printable test sets. Students practise gradients, parallel lines, perpendicular lines, missing coordinates, translations, and line relationships.
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