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5.15F Equation of a Line: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 65 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out y when x = 4 for the equation y = 2x + 3.

(Total for Question 1 is 1 mark)

Work out x when y = 10 for the equation y = 3x - 5.

(Total for Question 2 is 1 mark)

Find the gradient of the line passing through the points (1, 2) and (4, 8).

(Total for Question 3 is 1 mark)

Write down the equation of the line with gradient 1/2 that passes through the point (0, -3). Give your answer in the form y = mx + c.

(Total for Question 4 is 2 marks)

The line has equation y = -x + 4.
Part (a) Work out y when x = 2.
Part (b) Work out y when x = -1.

(a)Work out y when x = 2.(1)

(b)Work out y when x = -1.(1)

(Total for Question 5 is 2 marks)

Solve 2x + 3 = -x + 9.

(Total for Question 6 is 2 marks)

Given y = 3x - 6, work out the x-intercept and the y-intercept of this line.

(Total for Question 7 is 2 marks)

A taxi company charges a fixed flag drop of 2.50 pounds plus 0.80 pounds for each kilometre. The fare is given by F = 2.50 + 0.80d, where d is the distance in kilometres and F is the fare in pounds.
Part (a) Calculate the fare for a 10 km journey.
Part (b) Find the distance d when the fare is 10.00 pounds. Give your answer to 1 decimal place if needed.

(a)Calculate the fare for a 10 km journey.(1)

(b)Find the distance d when the fare is 10.00 pounds.(2)

(Total for Question 8 is 3 marks)

The line l has equation y = -1/2 x + 4.
Find the equation of the line m that is parallel to l and passes through the point (4, 1). Give your answer in the form y = mx + c.

(Total for Question 9 is 2 marks)

A line passes through the point (2, 5) and has a y-intercept of 1. Find the equation of the line in the form y = mx + c.

(Total for Question 10 is 2 marks)

Find the equation of the line passing through the points (-1, 2) and (3, 10). Give your answer in the form y = mx + c.

(Total for Question 11 is 3 marks)

A line has equation y = 4x - 7. State whether the point (3, 5) lies on this line. Show your working.

(Total for Question 12 is 2 marks)

Mark scheme · 5.15F Equation of a Line: Foundation Tier Practice

Question 1

B1 y = 11 cao
Answer: 11

Question 2

B1 x = 5 cao
Answer: 5

Question 3

B1 gradient = 2 cao
Answer: 2

Question 4

M1 substitute gradient and point into y = mx + c to find c, or state c = -3
A1 y = 1/2 x - 3 cao
Answer: y = 1/2 x - 3

Question 5

(a) B1 y = 2 cao
(a) Answer: 2
(b) B1 y = 5 cao
(b) Answer: 5

Question 6

M1 collect terms to get 3x = 6 or equivalent method
A1 x = 2 cao
Answer: 2

Question 7

M1 find x-intercept by setting y = 0 to get x = 2, or find y-intercept as c = -6
A1 x-intercept (2, 0) and y-intercept (0, -6) cao
Answer: x-intercept (2, 0); y-intercept (0, -6)

Question 8

(a) B1 F = 10.50 cao
(a) Answer: 10.50
(b) M1 set up 10.00 = 2.50 + 0.80d and isolate d
(b) A1 d = 9.375 so d = 9.4 km awrt
(b) Answer: 9.4 km

Question 9

M1 use same gradient -1/2 and substitute point to find c
A1 y = -1/2 x + 3 cao
Answer: y = -1/2 x + 3

Question 10

M1 find gradient m = (5 - 1)/(2 - 0) = 2 or equivalent method
A1 y = 2x + 1 cao
Answer: y = 2x + 1

Question 11

M1 find gradient m = (10 - 2)/(3 - (-1)) = 8/4 = 2
M1 substitute a point into y = 2x + c to find c
A1 y = 2x + 4 cao
Answer: y = 2x + 4

Question 12

M1 substitute x = 3 into y = 4x - 7 to get y = 5
A1 yes, (3, 5) lies on the line cao
Answer: Yes, (3, 5) lies on the line since y = 4(3) - 7 = 5.

Equation of a Line: Foundation Tier Practice - Worksheets, Questions and Revision