Printable · GCSE Foundation · ages 14-16

Gradients and intercepts of linear functions worksheet — GCSE Foundation

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 Foundation

Maths · GCSE Foundation · A10 · Gradients and intercepts of linear functions · Non-calculator · 15 questions

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1.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
(a)1
(b)−1
(c)3
(d)4
2.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.
3.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
4.Work out the gradient of the straight line with equation 2x + y = 8.
(a)−1/2
(b)8
(c)2
(d)−2
5.Write down the gradient of the line with equation y = 6 + 4x.
(a)6
(b)24
(c)10
(d)4
6.Work out the gradient of the straight line with equation 3y = 12 − 6x.
(a)2
(b)4
(c)−2
(d)−6
7.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.
(a)2
(b)4
(c)10
(d)0.5
8.Write down the y-intercept of the line with equation y = 3x + 8.
y = 3x + 8
(a)−8
(b)11
(c)3
(d)8
9.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
10.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.
(a)0.25
(b)4
(c)9
(d)36
11.Write down the gradient of the line with equation y = 7x − 2.
y = 7x − 2
(a)−7
(b)7
(c)2
(d)−2
12.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
13.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.
(a)There is not enough information
(b)They are equally steep
(c)Line D
(d)Line C
14.A straight line has equation y = 4 − 3x. Work out the gradient of the line.
(a)4
(b)−4
(c)3
(d)−3
15.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

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