Linear Functions

Question 0

Complete the table of values using the following linear function:
y = 3x + 2

x -2 -1 0 1 2
y

Answer 0

x -2 -1 0 1 2

y -4 -1 2 5 8

Question 1

For the linear function y = 3x + 2, what is:

• The independent variable?
• The dependent variable?

Answer 1

• X

- Y

Question 2

Complete the table of values using the linear function: y = 4 - 3x

x -2 -1 0 1 2
y

Answer 2

x -2 -1 0 1 2

y 10 7 4 1 -2

Question 3

For each linear function, write down its gradient and y intercept:

A) y = -3x + 7
B) y = 5 - x
C) y = 1/2x - 3

Answer 3

A) -3, 7
B) -1, 5
C) 1/2, -3

Question 4

The table below shows the quarterly cost of water usage for different volumes of water.

Volume, v (kL) 16 25 48 60 81 99
Cost, C ($) 168.24 183 220.72 240.40 274.84 304.36

A) What is the independant variable and what does it represent?
B) Find a linear function for C in terms of v.
C) What does the gradient represent?
D) What does the vertical intercept represent?
E) What is the cost of using 54 kL of water?
F) Find the volume of water usage that costs $265.

Answer 4

A) v, volume of water.
B) C = 1.64v + 142
C) Cost in dollars per kilolitre of water.
D) Fixed cost of water usage (even when no water is used).
E) $230.56

Question 5

What is the linear function for this table of values?

x 4 7 12 20
y 10 31 66 122

A) y= 1/7x - 18
B) y= 1/7x + 10
C) y= 7x - 1
D) y= 7x - 18

Answer 5

D

Question 6

Find the linear function for each table of values.

A) k 6 10 13 15
c 152 120 96 80

B) t 1 3 6 14
v 9 21 39 87

C) n 3 8 20 35
p 141 126 90 45

D) x 2 5 11 18
t -2 13 43 78

Answer 6

A) c= -8k + 200
B) v= 6t + 3
C) p= -3n + 150
D) t= 5x - 12

Question 10

On a road trip, the total distance travelled, D km, varies directly as the time, t hours.

Time, t (hours) 0 2 3 5 8
Distance travelled, D (km) 0 160 240 400 640

A) Find the equation for D in terms of t.
B) Find the time it takes to travel 550km, in hours and minutes correct to the nearest minute.

Answer 10

A)

B)