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Straight Line Graphs: y = mx + c - Worksheets, Questions and Revision

24 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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This topic is chapter 3 of KS3 Maths: Algebra Practice Book 2.

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KS3 · Algebra

2.16 Straight Line Graphs: y = mx + c

Calculators not allowed · about 65 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A line through (0, -3) and (2, 1) is drawn. Find its equation in the form y = mx + c.
(2)
2
The graph of a line is shown passing through (1, 4) and (4, 1). Find the equation of the line in the form y = mx + c.
(3)
3
A straight line passes through points A(-2, 0) and B(2, 4). Work out the equation of the line in the form y = mx + c.
(3)
4
A line has equation y = 2x + 1. State the gradient and the y-intercept.
(1)
5
Draw the line y = x - 2 on a grid. Give the coordinates of two points on the line that you would plot.
(1)
6
The line y = 0.5x + 3 is drawn. What is the y-intercept? Give your answer as a coordinate point.
(1)
7
A line passes through the points (1, 2) and (3, 6). Calculate the gradient of this line.
(2)
8
A line has equation y = -2x + 5. A second line has equation y = -2x - 1. Explain whether the lines are parallel or not and why.
(2)
9
The line y = mx + 2 passes through the point (4, 10). Find the value of m.
(2)
10
A line has equation y = 3x + 4. State the gradient and the y-intercept.
(1)
11
Given the line y = 5x - 8, a student plots the point (3, 6) and says it lies on the line. Is the student correct? Show your working.
(3)
12
A line has equation y = x/2 - 1. State the gradient and the y-intercept.
(1)
13
A line passes through the points (2, 5) and (6, 13). Find the equation of the line in the form y = mx + c. Then determine whether the point (10, 20) lies on this line.
(3)
14
Line L1 has equation y = 4x - 3. Line L2 passes through the point (0, 5) and is parallel to L1. Find the equation of L2.
(3)
15
A line crosses the x-axis at (5, 0) and has gradient 2. Find the equation of the line in the form y = mx + c, then state where it crosses the y-axis.
(3)
16
Two points lie on a line: (-3, 4) and (1, -8). Find the equation of the line in the form y = mx + c.
(3)
17
For the line y = -2x + 7, calculate y when x = 0 and when x = 3. Give both values.
(1)
18
The line y = 0.25x + 6 is drawn. What is the y-intercept? Give your answer as a coordinate point.
(1)
19
A line passes through the points (1, 3) and (4, 9). Calculate the gradient of this line.
(2)
20
Find the equation of the line with gradient 4 and y-intercept -3. Write your answer in the form y = mx + c.
(2)
21
A line has equation y = -3x + 8. A second line has equation y = -3x - 2. Explain whether the lines are parallel or not, and why.
(2)
22
The line y = mx + 2 passes through the point (2, 10). Find the value of m.
(2)
23
A line through (0, -5) and (4, 3) is drawn. Find its equation in the form y = mx + c.
(3)
24
The graph of a line is shown passing through (1, 6) and (4, 0). Find the equation of the line in the form y = mx + c.
(3)
Mark scheme · 2.16 Straight Line Graphs: y = mx + c

Question 1

  • M1 Find gradient: (1 - (-3))/(2 - 0) = 4/2 = 2 or equivalent
  • A1 y = 2x - 3 cao
  • Answer: y = 2x - 3

Question 2

  • M1 Calculate gradient using (1 - 4)/(4 - 1) or (change in y)/(change in x)
  • M1 Obtain gradient m = -1
  • A1 Substitute to find c and give equation y = -x + 5 cao
  • Answer: y = -x + 5

Question 3

  • M1 Use gradient formula: (4 - 0)/(2 - (-2)) or equivalent
  • M1 Find gradient m = 1
  • A1 Substitute to find c = 2 and give equation y = x + 2 cao
  • Answer: y = x + 2

Question 4

  • B1 Gradient = 2 and y-intercept = 1 (or stated as (0, 1)) cao
  • Answer: gradient 2, y-intercept 1

Question 5

  • B1 Two correct points on the line, e.g. (0, -2) and (2, 0) or equivalent cao
  • Answer: (0, -2) and (2, 0)

Question 6

  • B1 y-intercept (0, 3) cao
  • Answer: (0, 3)

Question 7

  • M1 Use gradient formula (change in y)/(change in x) = (6 - 2)/(3 - 1) or equivalent
  • A1 Gradient = 2 cao
  • Answer: 2

Question 8

  • M1 States that gradients are equal (both -2) or states property of parallel lines
  • A1 Concludes the lines are parallel because they have the same gradient (different intercepts) cao
  • Answer: They are parallel because both have gradient -2 (different y-intercepts).

Question 9

  • M1 Substitute x=4, y=10 into y = mx + 2 leading to 10 = 4m + 2 or equivalent
  • A1 m = 2 cao
  • Answer: 2

Question 10

  • B1 gradient 3, y-intercept (0, 4)
  • Answer: gradient = 3, y-intercept = (0, 4)

Question 11

  • M1 substitutes x = 3 into y = 5x - 8
  • A1 finds y = 7
  • B1 correct conclusion: the student is incorrect, since 7 does not equal 6
  • Answer: No, when x = 3, y = 7, not 6

Question 12

  • B1 gradient 1/2, y-intercept (0, -1)
  • Answer: gradient = 1/2, y-intercept = (0, -1)

Question 13

  • M1 correct gradient method, gradient = 2
  • A1 y = 2x + 1 cao
  • B1 correct conclusion: (10, 20) does not lie on the line, since 2(10) + 1 = 21
  • Answer: y = 2x + 1; (10, 20) does not lie on the line

Question 14

  • M1 identifies that parallel lines share gradient 4
  • M1 uses the point (0, 5) to find c = 5
  • A1 y = 4x + 5 cao
  • Answer: y = 4x + 5

Question 15

  • M1 substitutes (5, 0) into y = 2x + c to find c = -10
  • A1 y = 2x - 10 cao
  • B1 y-intercept (0, -10) (ft their equation)
  • Answer: y = 2x - 10; y-intercept (0, -10)

Question 16

  • M1 correct gradient method, gradient = -3
  • M1 substitutes a point to find c, e.g. -8 = -3(1) + c
  • A1 y = -3x - 5 cao
  • Answer: y = -3x - 5

Question 17

  • B1 y = 7 and y = 1
  • Answer: y = 7 when x = 0; y = 1 when x = 3

Question 18

  • B1 (0, 6) cao
  • Answer: (0, 6)

Question 19

  • M1 correct method, e.g. (9 - 3) / (4 - 1)
  • A1 2 cao
  • Answer: 2

Question 20

  • M1 identifies m = 4 and c = -3
  • A1 y = 4x - 3 cao
  • Answer: y = 4x - 3

Question 21

  • M1 compares the gradients of both lines
  • A1 parallel, because both lines have gradient -3
  • Answer: Parallel, because both have gradient -3

Question 22

  • M1 substitutes (2, 10) into y = mx + 2
  • A1 m = 4 cao
  • Answer: m = 4

Question 23

  • M1 correct gradient method, e.g. (3 - (-5)) / (4 - 0)
  • A1 gradient = 2
  • A1 y = 2x - 5 cao (using the y-intercept given by (0, -5))
  • Answer: y = 2x - 5

Question 24

  • M1 correct gradient method, e.g. (0 - 6) / (4 - 1)
  • M1 substitutes a point to find c, e.g. 6 = -2(1) + c
  • A1 y = -2x + 8 cao
  • Answer: y = -2x + 8

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