Connect a table of coordinates, a plotted straight line and its equation. Practise finding gradients and intercepts, then interpreting what they tell you.
Foundation and Higher · Useful for students strengthening core skills before mixed GCSE practice.
Core pathway. Core GCSE methods are useful across Foundation and Higher. Start with the core examples and questions.
Higher extension. More demanding selections are marked Higher extension: practice questions 2, 8. Use these after the core work, following your teacher’s guidance.
3 worked examples and 8 original practice questions · Allow 25–40 minutes · Read online or print. Higher extensions are labelled. No account or email needed.
Printing includes the method, examples and space for working, followed by a separate answer section.
A useful approach
Read each axis scale carefully and calculate coordinate pairs before plotting.
Gradient is the change in y divided by the change in x, using two points on the line.
In y = mx + c, m is the gradient and c is the y-intercept. Substitute a known point to check the equation.
A mistake to watch for
A negative gradient means y falls as x increases. Keep the order of subtraction the same in both coordinate differences.
Learn each method, then practise it
Read each line of working and explain why it follows from the previous line.
Plot a straight line
Calculate coordinate pairs, check the axis scales, plot the points and join them with one straight line. A third point provides a check.
Worked example 1
Drawing Linear Graphs · Core GCSE skill · Calculator allowed · 3 marks
On the grid, draw the graph of y = 2x − 3 for values of x from −2 to 3
Diagram for Drawing Linear Graphs. The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. On the grid, draw the graph of y = 2 x minus 3 for values of x from minus 2 to 3 Horizontal axis from -2 to 3. Vertical axis from -8 to 4. Use the labelled information; do not estimate measurements from the sketch.
Make a table of values: x = -2 gives y = -7, x = 0 gives y = -3, x = 1 gives y = -1, x = 3 gives y = 3
Plot the points and join them with a single straight line with a ruler
Answer: Straight line through (-2, -7), (0, -3) and (3, 3)
Model diagram: compare the plotted points or labelled working with your method.Read a text description of this diagram
Worked diagram. On the grid, draw the graph of y = 2 x minus 3 for values of x from minus 2 to 3 Horizontal axis from -2 to 3. Vertical axis from -8 to 4. Model working: Make a table of values: x = -2 gives y = -7, x = 0 gives y = -3, x = 1 gives y = -1, x = 3 gives y = 3 Plot the points and join them with a single straight line with a ruler
Write your working on paper. Marks indicate how much working to show; these questions are self-marked and do not change saved practice results. Use squared paper for drawing questions.
Question 1
Drawing Linear Graphs · Core GCSE skill · Calculator allowed · 3 marks
On the grid, draw the graph of x + y = 6 for values of x from 0 to 6
Diagram for Drawing Linear Graphs. The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. On the grid, draw the graph of x + y = 6 for values of x from 0 to 6 Horizontal axis from 0 to 6. Vertical axis from 0 to 6. Use the labelled information; do not estimate measurements from the sketch.
Drawing Linear Graphs · Higher extension · Calculator allowed · 4 marks
Complete the table of values for y = 2 − 2x x: −2, −1, 0, 1, 2, 3 y: 6, ?, 2, 0, ?, −4
On the grid, draw the graph of y = 2 − 2x for values of x from −2 to 3
Diagram for Drawing Linear Graphs. The question states the required measurements and relationships.Read a text description of this diagram
Given diagram. Complete the table of values for y = 2 minus 2 x x : minus 2, minus 1, 0, 1, 2, 3 y : 6, ?, 2, 0, ?, minus 4 On the grid, draw the graph of y = 2 minus 2 x for values of x from minus 2 to 3 Horizontal axis from -2 to 3. Vertical axis from -5 to 7. Use the labelled information; do not estimate measurements from the sketch.
Compare the reasoning as well as the final answer. Another correct method is valid. If a step is unclear, revisit an example before trying a similar question.
Answer 1
Show answer and working for question 1
Rearrange to y = 6 - x
When x = 0, y = 6. When x = 3, y = 3. When x = 6, y = 0
Plot the points and join them with a single straight line with a ruler
Answer: Straight line through (0, 6) and (6, 0)
Model diagram: compare the plotted points or labelled working with your method.Read a text description of this diagram
Worked diagram. On the grid, draw the graph of x + y = 6 for values of x from 0 to 6 Horizontal axis from 0 to 6. Vertical axis from 0 to 6. Model working: Rearrange to y = 6 - x When x = 0, y = 6. When x = 3, y = 3. When x = 6, y = 0 Plot the points and join them with a single straight line with a ruler
b) Plot all six points and join them with a single straight line with a ruler. The line slopes downwards from left to right
Answer: (a) 4 and -2 (b) Straight line through (-2, 6), (0, 2) and (3, -4)
Model diagram: compare the plotted points or labelled working with your method.Read a text description of this diagram
Worked diagram. Complete the table of values for y = 2 minus 2 x x : minus 2, minus 1, 0, 1, 2, 3 y : 6, ?, 2, 0, ?, minus 4 On the grid, draw the graph of y = 2 minus 2 x for values of x from minus 2 to 3 Horizontal axis from -2 to 3. Vertical axis from -5 to 7. Model working: a) When x = -1, y = 2 - 2(-1) = 4 When x = 2, y = 2 - 2(2) = -2 b) Plot all six points and join them with a single straight line with a ruler. The line slopes downwards from left to right
Workouts provide interactive practice; choose the tier your school has recommended.
Use this in class
Give pupils squared paper or use the on-screen drawing tools in Topic Workout. Ask for an explanation of the scale and units before revealing the model.
Build a custom classroom worksheet or print this page. The teacher builder can display questions on a projector and reveal answers separately.