Linear Functions and Graphs

Question 1

(i) On a sheet of graph paper, using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis, draw the graph of the function y = 2x for values
of x from 0 to 4.
(ii) The point (3, p) lies on the graph in part (i). Find the value of p.

Answer 1

(ii) From the graph in part (i), when x = 3, p = y = 6.

Question 2

what is y = mx + c

Answer 2

equation of a straight line

Question 3

(a) The equation of a straight line is y = 2x - 1. State its gradient and y-intercept.
(b) A line has gradient -3 and y-intercept 4. State its equation.

Answer 3

(a) Line: y = 2x - 1
Gradient = 2; y-intercept = -1
(b) The equation of the straight line is y = - 3x + 4.

Question 4

Answer 4

(a) 3
(b) -3/2

Question 5

Answer 5

Question 6

The travel graph shows a journey taken by a cyclist. He started his 50-km journey at 0800 hours. At 0900 hours, he spent half an hour replacing a punctured tyre. He then continued his journey and reached his destination at 1130 hours.
(i) How far did the cyclist travel before his bicycle tyre was punctured?
(ii) Find the gradient of each of the following line segments, stating dearly what each gradient represents.

(a) OA (b) AB (c) BC

Answer 6

(i) 20km
(ii)
(a) Gradient of OA = 20 km/1h = 20 km/h
This means that the average speed of the cyclist from O to A was 20 km/h.
(b) Gradient of AB = 0
This means that the average speed of the cyclist from A to B was 0km/h,
i.e. he was stationary.
(c) Gradient of BC = 30 km/2h = 15km/h
This means that the average speed of the cyclist from B to C was 15km/h.