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Gradients and intercepts of linear functions worksheet — GCSE Higher

Fifteen questions on "gradients and intercepts of linear functions" — DfE statement A10. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Gradients and intercepts of linear functions worksheet — GCSE Higher

Maths · GCSE Higher · A10 · Gradients and intercepts of linear functions · 15 questions

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1.Work out the gradient of the straight line with equation y = (2x/5) − 3.
(a)2/5
(b)5/2
(c)−2/5
(d)−3
2.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.
(a)0.05
(b)20
(c)100
(d)25
3.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?
(a)The total cost for a job lasting 1 hour.
(b)The hourly rate the plumber charges.
(c)The number of hours worked before charging starts.
(d)The fixed call-out fee, charged before the hourly rate.
4.A straight line has equation y = 4 − 3x. Work out the gradient of the line.
(a)4
(b)−4
(c)3
(d)−3
5.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.
(a)2
(b)−0.5
(c)0.5
(d)−0.8
6.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?
(a)The cost, in pounds, for each extra 2 gigabytes of data used
(b)The fixed monthly fee, in pounds
(c)The cost, in pounds, for each extra gigabyte of data used
(d)The total number of gigabytes included in the plan
7.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.
(a)20
(b)456
(c)0.05
(d)480
8.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.
(a)−3
(b)−2
(c)3
(d)6
9.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.
y = 2x + 4
(a)(4, 0)
(b)(−2, 0)
(c)(0, 2)
(d)(0, 4)
10.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.
y = 12x + 20
(a)12
(b)3
(c)20
(d)5
11.Work out the gradient of the straight line with equation 2x + y = 8.
(a)−1/2
(b)8
(c)2
(d)−2
12.Write down the gradient of the line with equation y = −x + 3.
y = −x + 3
(a)−3
(b)−1
(c)3
(d)1
13.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.
y = 2x − 6
(a)(−3, 0)
(b)(6, 0)
(c)(0, −6)
(d)(3, 0)
14.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.
y = 2x + 1y = -2x + 3
(a)Yes, because the gradients 2 and −2 add to 0
(b)No, because their gradients are 2 and −2
(c)Yes, because both gradients have size 2
(d)No, because their y-intercepts are 1 and 3
15.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.
y = -5x + 200
(a)(40, 0)
(b)(0, 40)
(c)(0, 200)
(d)(200, 0)

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