Make a table of values, plot the points accurately and draw a straight-line graph with a ruler. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A straight line y=mx+c has gradient m (rise over run) and y-intercept c (where it cuts the y-axis). To draw it, make a table of three x values, compute y, plot, and join with a ruler. Three points catch a mis-plotted middle.
To draw x+2y=8 without rearranging, find the intercepts: x=0 gives y=4, y=0 gives x=8, and a third point as a check. The line x=3 is vertical; y=−2 is horizontal. Label the line with its equation.
Make a table of at least three x values (include a negative and zero), plot, join with a ruler. The y-intercept is the value when x=0; the gradient is how many y you go up for one x across. Rearrange x+y=5 to y=5−x before you table it.
Objectives
Pick three x-values, often −1, 0 and 1, or 0, 1 and 2.
Plot the points and join them with a ruler.
m is how much y increases when x increases by 1.
Key points
Complete a table of values for an equation like y=2x−1.
Plot coordinates accurately and join them with a ruled straight line.
Rearrange equations such as 2x+y=6 into y= … form, or use the cover-up method.
Read values off the graph once it is drawn.
Worked examples
Example 1
The line is y = 2x + 1. What is y when x = −2?
2 marks
Substitute x = −2 into y = 2x + 1.
2 × (−2) = −4, so y = −4 + 1.
y = −3.
Answer: -3
Common slips
Slip: Substitute x = −2 into y = 2x + 1, but ignore the + 1. The constant is part of the equation, so it has to be used.
Slip: 2 × (−2) = −4. This only finds m × x, not m × x + c.
Slip: y = −4. The answer must include the constant.
Example 2
The line is y = 3x − 1. What is y when x = −2?
2 marks
Substitute x = −2 into y = 3x − 1.
3 × (−2) = −6, so y = −6 − 1.
y = −7.
Answer: -7
Common slips
Slip: Substitute x = −2 into y = 3x − 1, but ignore the − 1. The constant is part of the equation, so it has to be used.
Slip: 3 × (−2) = −6. This only finds m × x, not m × x + c.
Slip: y = −6. The answer must include the constant.
Example 3
The line is y = −x + 4. What is y when x = −2?
3 marks
Substitute x = −2 into y = −x + 4.
(−1) × (−2) = 2, so y = 2 + 4.
y = 6.
Answer: 6
Common slips
Slip: Substitute x = −2 into y = −x + 4, but ignore the + 4. The constant is part of the equation, so it has to be used.
Slip: (−1) × (−2) = 2. This only finds m × x, not m × x + c.
Slip: y = 2. The answer must include the constant.
Questions and answers
GCSE Maths drawing linear graphs questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
The line is y = 2x − 3. What is y when x = −2?
Show answer
Answer: -7
Substitute x = −2 into y = 2x − 3.
2 × (−2) = −4, so y = −4 − 3.
M1 — Substitute x = −2 into y = 2x − 3.
A1 — Answer -7
Question 2 Easy2 marks
The line is y = 2x + 1. What is y when x = −1?
Show answer
Answer: -1
Substitute x = −1 into y = 2x + 1.
2 × (−1) = −2, so y = −2 + 1.
M1 — Substitute x = −1 into y = 2x + 1.
A1 — Answer -1
Question 3 Medium2 marks
The line is y = 2x − 3. What is y when x = −1?
Show answer
Answer: -5
Substitute x = −1 into y = 2x − 3.
2 × (−1) = −2, so y = −2 − 3.
M1 — Substitute x = −1 into y = 2x − 3.
A1 — Answer -5
Question 4 Medium2 marks
The line is y = 2x + 1. What is y when x = 0?
Show answer
Answer: 1
Substitute x = 0 into y = 2x + 1.
2 × 0 = 0, so y = 0 + 1.
M1 — Substitute x = 0 into y = 2x + 1.
A1 — Answer 1
Question 5 Hard2 marks
The line is y = 2x − 3. What is y when x = 0?
Show answer
Answer: -3
Substitute x = 0 into y = 2x − 3.
2 × 0 = 0, so y = 0 − 3.
M1 — Substitute x = 0 into y = 2x − 3.
A1 — Answer -3
Question 6 Hard2 marks
The line is y = 2x + 1. What is y when x = 1?
Show answer
Answer: 3
Substitute x = 1 into y = 2x + 1.
2 × 1 = 2, so y = 2 + 1.
M1 — Substitute x = 1 into y = 2x + 1.
A1 — Answer 3
Question 7 Exam-style3 marks
The line is y = 2x − 3. What is y when x = 1?
Show answer
Answer: -1
Substitute x = 1 into y = 2x − 3.
2 × 1 = 2, so y = 2 − 3.
y = −1.
M1 — Substitute x = 1 into y = 2x − 3.
M1 — 2 × 1 = 2, so y = 2 − 3.
A1 — Answer -1
Common mistakes
Most lost marks on this topic are one slip.
Plotting x and y the wrong way round.
The first coordinate is across.
Using one point and guessing the slope.
Plot at least three points.
Reading the intercept from the x-axis.
c is on the y-axis.
Spot the slip
In y = 2x + 1, the line crosses the y-axis at
1
2
0
Show the slip
1 The constant term is the intercept.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Fill in the table completely — a fully correct table is usually worth a mark on its own.
One wrong point that is off the line is easy to spot: recheck that substitution.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.