Equation of a line Quiz (Grade 5)

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Equation of a line — Notes & Worked Examples Show / Hide

Explanation:

The equation of a straight line is written in the form y = mx + c, where m is the gradient and c is the y-intercept (the value of y where the line crosses the y-axis at (0, c)).

To find the equation of a line from two points, first calculate the gradient m = y₂ − y₁x₂ − x₁, then substitute m and the coordinates (x, y) of one point into y = mx + c to find c.

Example 1: Find the equation of the line with gradient 4 that passes through the point (2, 5).

Solution:

Start with y = 4x + c

Sub (2, 5): 5 = 4(2) + c

5 = 8 + c → c = −3

Answer: y = 4x − 3

Example 2: Find the equation of the line passing through (−2, 7) and (4, −5).

Solution:

Gradient m = −5 − 74 − (−2) = −126 = −2

Substitute m = −2 and (4, −5) into y = mx + c:

−5 = −2(4) + c → −5 = −8 + c → c = 3

Answer: y = −2x + 3

One Page Guide (PDF) Equation of a line Worksheets

Question 1

[1 mark]

Work out
A line has a gradient of 2 and a y-intercept of 2
Write down the equation of the line

y =

Worked Solution & Answer

y = mx + c, where m = change in ychange in x is the gradient and c is the y-intercept (where x = 0).
y = 2x + 2

Answer: y = y = 2x + 2

Question 2

[1 mark]

Find the equation of the line that passes through (0, -3) and has a gradient of 5

y =

Worked Solution & Answer

y = mx + c, where m = change in ychange in x is the gradient and c is the y-intercept (where x = 0).
y = 5x - 3

Answer: y = y = 5x - 3

Question 3 AQA Jun 2025 2H Q2

[2 marks]

Here are lines A and B.

Complete these statements.

Worked Solution & Answer

Vertical line A passes through x = 3, so its equation is x = 3. M1
Horizontal line B has gradient 0. A1

Answer: x = 3, 0

Question Paper (PDF) • Mark Scheme (PDF)

Question 4

[3 marks]

The straight line **L** is shown on the grid.

Find an equation for **L**.
Give your answer in the form y = mx + c

Worked Solution & Answer

y-intercept c = 3. Gradient m = (0 – 3) ÷ (4 – 0) = –3/4 = –0.75 M2
Equation: y = –3/4 x + 3. A1

Answer: y = -34x + 3

Question Paper (PDF) • Mark Scheme (PDF)

Question 5 IGCSE Jun 2023 1H Q13

[3 marks]

Work out
A is the point with coordinates (-5, 12)
B is the point with coordinates (19, -48)
Find an equation of the straight line that passes through the points A and B

y =

Worked Solution & Answer

Gradient m = (–48 – 12) ÷ (19 – –5) = –60 ÷ 24 = –2.5. Using (–5, 12): 12 = –2.5(–5) + c => 12 = 12.5 + c => c = –0.5. Equation: y = –2.5x – 0.5 (or 5x + 2y + 1 = 0). M2 A1

Answer: y = y = -2.5x - 0.5

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 AQA Jun 2019 3F Q28 / 3H Q12

[3 marks]

A straight line has gradient 4 and passes through the point (5, 23)

Work out the equation of the line.
Give your answer in the form y = mx + c

Answer

Worked Solution & Answer

y = mx + c ⇒ y = 4x + c M1
Substitute (5, 23): M1
23 = 4(5) + c = 20 + c ⇒ c = 3
Equation is y = 4x + 3. A1

Answer: Answer y = 4x + 3

Question Paper (PDF) • Mark Scheme (PDF)

Question 7 Specimen Set 1 3F Q23 / 3H Q3

[3 marks]

Line L is drawn on the grid below.

Find the equation for the straight line L.
Give your answer in the form y = mx + c

Worked Solution & Answer

Gradient m = (5 – 1) / (2 – 0) = 2 M2
y-intercept c = 1 ⇒ y = 2x + 1 A1

Answer: y = 2x + 1

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 IGCSE Jun 2024 1HR Q9 / 1FR Q24

[3 marks]

Line L is drawn on the grid.

Find an equation for L
Give your answer in the form y = mx + c

Worked Solution & Answer

y-intercept c = 1 M1
passes through (0, 1) and (2, 0) ⇒ gradient m = (0 − 1)/(2 − 0) = −1/2 M1
Equation: y = −0.5x + 1 A1

Answer: y = -12x + 1

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 OCR Nov 2020 4H Q7

[3 marks]

This graph shows part of a straight line.

(a) Show that the gradient of the line is 2.5. [1 mark]

(b) Write down the equation of the line. [2 marks]

y =

Worked Solution & Answer

(a)

(Gradient = change in y ÷ change in x)
Pick two points on the line, e.g
(−2, −6) and (2, 4): gradient = (4 − (−6)) / (2 − (−2)) = 10 / 4 = 2.5. C1

Answer (a): Using (0, −1) and (2, 4): gradient = (4 − (−1)) ÷ (2 − 0) = 5 ÷ 2 = 2.5.

(b)

Gradient m = 2.5 and y-intercept c = −1 M1
⇒ y = 2.5x − 1. A1

Answer (b): y = y = 2.5x - 1

Question Paper (PDF) • Mark Scheme (PDF)

Question 10 OCR Nov 2023 2F Q24

[4 marks]

A straight line passes through the points (0, 5) and (2, 13).

Find the equation of the line in the form y = mx + c.

y =

Worked Solution & Answer

Gradient m = (13 − 5) ÷ (2 − 0) = 8 ÷ 2 = 4. M2
y-intercept c = 5. M1
Equation of line: y = 4x + 5. A1

Answer: y = y = 4x + 5

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 26 marks)

Equation of a line Worksheets Next: Spheres and cones →

Grade 5 Quizzes

25 Topics

5A - Combining ratios	5B - Direct and inverse proportion
5C - Reverse percentages	5D - Standard form
5E - Speed	5F - Changing the subject
5G - Quadratic expressions	5H - Solving quadratic equations
5J - Drawing quadratic graphs	5K - Cubic/reciprocal graphs
5L - Simultaneous equations	5M - Sector areas and arc lengths
5N - Sim. equ. graphically	5P - Midpoint of a line segment
5Q - Gradient of a line	5R - Equation of a line
5S - Spheres and cones	5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)	5V - Exact trig. values
5W - Probability trees	5X - Vectors
5Y - Venn diagrams	5Z - Density
5AA - Pressure