Question

Write a function rule for each table.

Days
1
2
3
4
cost to rent a truck
34
57
80
103



the choices are:
(A)c=23d

(B)c=23d+11

(C) c=11d+23

(D)c=23d+23

Answer 1

Let's assume that this function is linear.

Take any 2 of the points and find the slope of the line segment connecting them:

103 - 80
m = ------------- = 23, meaning $23 per day. Subtracting $23 from $34 (in the table), we get $11. Thus, the correct linear relationship is B.
4 - 3

Answer 2

`y=23x+11`

Explanation:

Days cost to rent a truck

1 34

2 57

3 80

4 103

The difference of cost of rent is 23

57-34= 23

80-57=23

Since the difference is a constant, it is a linear function

To find the rule of linear function we use y=mx+b

where m is the slope and b is the initial value

Slope is the constant that is 23

So equation becomes
`y=23x+b`

To find out b we plug in days x=1 and cost y= 34

`34=23(1)+b`

Subtract 23 from both sides

`b=11`

The function rule for this table is

`y=23x+11`