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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.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.
y = 3x + 6
(a)(2, 0)
(b)(−2, 0)
(c)(6, 0)
(d)(0, 6)
2.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
3.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
4.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
5.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)
6.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.
(a)3 km/h
(b)60 km/h
(c)195 km/h
(d)180 km/h
7.A straight line has equation y = 4 − 3x. Work out the gradient of the line.
(a)4
(b)−4
(c)3
(d)−3
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.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
10.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
11.Work out the gradient of the straight line with equation 2x + y = 8.
(a)−1/2
(b)8
(c)2
(d)−2
12.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
13.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
14.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)
15.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.

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