The diagram shows two straight lines, A and B, drawn on a grid.
(a)Line A is parallel to the x-axis and passes through the point (0, 5). Write down the equation of line A.(1)
(b)Line B is parallel to the y-axis and passes through the point (-2, 0). Write down the equation of line B.(1)
(Total for Question 2 is 2 marks)
3
Circle the correct point in each case.
(a)Which of these points lies on the line with equation y = 2x + 1?(1)
A) (1, 2)
B) (2, 4)
C) (3, 7)
D) (0, 0)
(b)Which of these points lies on the line with equation y = 3x - 2?(1)
A) (1, 1)
B) (2, 3)
C) (0, 5)
D) (-1, 0)
(Total for Question 3 is 2 marks)
4
A straight line has equation y = x - 1.
(a)Complete the table of values for y = x - 1.(1)
(b)Write down the coordinates of two points that lie on the line y = x - 1.(1)
(Total for Question 4 is 2 marks)
5
Complete the table of values for y = 2x - 1 and use it to draw the graph of y = 2x - 1 for values of x from -2 to 2.
(Total for Question 5 is 3 marks)
6
Draw the graph of y = 3x + 2 for values of x from -2 to 2. You must show your table of values.
(Total for Question 6 is 3 marks)
7
On the grid provided, draw the following straight lines.
(a)Draw the graph of x = -3.(1)
(b)Draw the graph of y = 2.(1)
(Total for Question 7 is 2 marks)
8
A straight line has equation y = 5x - 3.
(a)Write down the gradient of the line.(1)
(b)Write down the coordinates of the point where the line crosses the y-axis.(1)
(Total for Question 8 is 2 marks)
9
Which equation represents a straight line with gradient 4 and y-intercept -2?
A) y = 4x - 2
B) y = -2x + 4
C) y = 4x + 2
D) y = 2x - 4
(Total for Question 9 is 1 mark)
10
A straight line has equation y = -2x + 1.
(a)Complete the table of values for y = -2x + 1.(2)
(b)Draw the graph of y = -2x + 1 on the grid, for values of x from -2 to 2.(2)
(Total for Question 10 is 4 marks)
11
The diagram shows a straight line drawn on a grid. The line passes through the points (0, 2) and (4, 10).
(a)Work out the gradient of the line.(1)
(b)Write down the y-intercept of the line.(1)
(c)Write down the equation of the line.(1)
(Total for Question 11 is 3 marks)
12
The diagram shows the graph of y = 4x - 3 drawn on a grid, for values of x from -2 to 3.
(a)Use the graph to find the value of y when x = 1.5(1)
(b)Use the graph to find the value of x when y = 0(1)
(Total for Question 12 is 2 marks)
13
A straight line has equation y = 0.5x + 3.
(a)Complete the table of values for y = 0.5x + 3.(1)
(b)Draw the graph of y = 0.5x + 3 on the grid, for values of x from -4 to 4.(2)
(Total for Question 13 is 3 marks)
14
A straight line has equation 2x + y = 8.
(a)Rearrange 2x + y = 8 to make y the subject.(2)
(b)Complete a table of values for x = 0, 1, 2, 3, 4 and draw the graph of 2x + y = 8 on the grid.(2)
(Total for Question 14 is 4 marks)
15
A straight line has equation 3x - 2y = 12.
(a)Find the coordinates of the point where the line crosses the x-axis.(1)
(b)Find the coordinates of the point where the line crosses the y-axis.(1)
(c)Draw the graph of 3x - 2y = 12 on the grid.(1)
(Total for Question 15 is 3 marks)
16
Determine whether the point (3, 7) lies on the line with equation y = 4x - 5. Show your working.
(Total for Question 16 is 2 marks)
17
Find the coordinates of the midpoint of the line segment joining the points A(-3, 5) and B(5, -1).
(Total for Question 17 is 2 marks)
18
A straight line passes through the point (0, 4) and has gradient -3.
(a)Write down the equation of the line.(1)
(b)Draw the graph of the line on the grid, for values of x from -2 to 3.(2)
(Total for Question 18 is 3 marks)
19
Line L1 has equation y = 2x - 5. Line L2 is parallel to L1 and passes through the point (0, 3).
(a)Write down the equation of line L2.(1)
(b)Show that the point (4, 10) does not lie on line L2.(2)
(Total for Question 19 is 3 marks)
20
The diagram shows the graphs of y = x + 1 and y = -2x + 7 drawn on the same grid, intersecting at a single point. Use the graphs to write down the solution to the simultaneous equations y = x + 1 and y = -2x + 7.
(Total for Question 20 is 2 marks)
Mark scheme · 3.15 Drawing Linear Graphs
Question 1
B1 correct table values 2, 3, 5 (all three correct)
B2 correct straight line drawn from (-2,2) to (2,6) (B1 for at least 4 of the 5 points correctly plotted if the line is not fully correct)
Answer: Table values: 2, 3, 5. Straight line through (-2,2), (-1,3), (0,4), (1,5), (2,6).
Question 2
(a) B1 y = 5 cao
(a) Answer: y = 5
(b) B1 x = -2 cao
(b) Answer: x = -2
Question 3
(a) B1 C cao
(a) Answer: C) (3, 7)
(b) B1 A cao
(b) Answer: A) (1, 1)
Question 4
(a) B1 both missing values correct: 0 and 1
(a) Answer: x = 1 gives y = 0; x = 2 gives y = 1
(b) B1 any two correct coordinate pairs from the table, ft candidate's table
(b) Answer: e.g. (1, 0) and (2, 1)
Question 5
B1 all five table values correct: -5, -3, -1, 1, 3
B2 correct straight line drawn through the plotted points (B1 for at least 4 points correctly plotted if the line is not fully correct)
Answer: Table: -5, -3, -1, 1, 3. Line through (-2,-5), (-1,-3), (0,-1), (1,1), (2,3).
Question 6
B1 at least 3 correct points from a table of values for y = 3x + 2
B2 correct straight line drawn through the points (B1 for a line that is only partially correct or too short)
Answer: Points: (-2,-4), (-1,-1), (0,2), (1,5), (2,8); straight line through all of them.
Question 7
(a) B1 correct vertical line drawn through x = -3
(a) Answer: Vertical line through every point with x-coordinate -3.
(b) B1 correct horizontal line drawn through y = 2
(b) Answer: Horizontal line through every point with y-coordinate 2.
Question 8
(a) B1 5 cao
(a) Answer: 5
(b) B1 (0, -3) oe -3 cao
(b) Answer: (0, -3)
Question 9
B1 A cao
Answer: A) y = 4x - 2
Question 10
(a) B1 at least 2 of the 3 missing values correct
(a) B1 all 3 missing values correct: 3, 1, -1
(a) Answer: x = -1 gives y = 3; x = 0 gives y = 1; x = 1 gives y = -1
(b) B1 all 5 points correctly plotted ft candidate's table
(b) B1 correct straight line drawn through the points
(b) Answer: Line through (-2,5), (-1,3), (0,1), (1,-1), (2,-3).
Question 11
(a) M1 (10 - 2) / (4 - 0) = 2 cao
(a) Answer: 2
(b) B1 2 cao
(b) Answer: 2
(c) B1 y = 2x + 2 oe, ft parts (a) and (b)
(c) Answer: y = 2x + 2
Question 12
(a) B1 awrt 3 ft reading from graph
(a) Answer: 3
(b) B1 awrt 0.75 ft reading from graph
(b) Answer: 0.75
Question 13
(a) B1 all three missing values correct: 2, 4, 5
(a) Answer: x = -2 gives y = 2; x = 2 gives y = 4; x = 4 gives y = 5
(b) B1 all 5 points correctly plotted ft candidate's table
(b) B1 correct straight line drawn through the points
(b) Answer: Line through (-4,1), (-2,2), (0,3), (2,4), (4,5).
Question 14
(a) M1 subtracts 2x from both sides oe
(a) A1 y = -2x + 8 oe cao
(a) Answer: y = -2x + 8
(b) B1 all 5 points correctly plotted ft part (a): (0,8), (1,6), (2,4), (3,2), (4,0)
(b) B1 correct straight line drawn through the points
(b) Answer: Line through (0,8), (1,6), (2,4), (3,2), (4,0).
Question 15
(a) M1 substitutes y = 0 to get (4, 0) cao
(a) Answer: (4, 0)
(b) M1 substitutes x = 0 to get (0, -6) cao
(b) Answer: (0, -6)
(c) B1 correct straight line drawn through (4,0) and (0,-6), ft parts (a) and (b)
(c) Answer: Straight line through (4, 0) and (0, -6).
Question 16
M1 substitutes x = 3 into the equation: 4(3) - 5
A1 7 = 7 so yes, the point does lie on the line, cso
Answer: Yes, the point (3, 7) lies on the line.
Question 17
M1 ((-3 + 5)/2, (5 + (-1))/2) oe
A1 (1, 2) cao
Answer: (1, 2)
Question 18
(a) B1 y = -3x + 4 oe cao
(a) Answer: y = -3x + 4
(b) B1 correct points plotted ft part (a): (-2,10), (-1,7), (0,4), (1,1), (2,-2), (3,-5)
(b) B1 correct straight line drawn through the points
(b) Answer: Line through (-2,10), (-1,7), (0,4), (1,1), (2,-2), (3,-5).
Question 19
(a) B1 y = 2x + 3 oe cao
(a) Answer: y = 2x + 3
(b) M1 substitutes x = 4 into the equation of L2: 2(4) + 3
(b) A1 11 does not equal 10, so the point does not lie on L2, cso
(b) Answer: y = 11 when x = 4, and 11 does not equal 10, so (4, 10) does not lie on L2.
Question 20
M1 identifies the point of intersection of the two lines on the graph