Question

The table and graph represents two different bus to come showing the cost as a linear function of the number of people in the group. Which description best compares the two functions?

Answer 1

Answer:

The description that best compares the two functions is:

           The functions have the same initial value.

Step-by-step explanation:

We are given the table for Tour 1 as:

                People           cost($)

                    1                    45

                    2                   55

                    3                   65

                    4                    75

The function that represents these points is given by:

             y=10x+35

where x represent people and y represent the cost of x people.

This means that the rate of  change is: 10

and initial value i.e. when x=0 is:  35

Tour 2  is given by:

     People       Cost ($)

        0                 35

        1                   50

        2                  65

        3                   80

        4                   95

Hence, we see that the initial value is: 35

and the rate of change of the function is: 15

(

Since,

$\dfrac{50-35}{1-0}=\dfrac{65-50}{2-1}=\dfrac{80-65}{3-2}=\dfrac{95-80}{4-3}=15$  )

• Hence, we see that the rate of change for Tour 2 is greater than Tour 1.

Answer 2

The functions have the same initial value. The table goes up by 10 per person so at 0, it would be 35 and on the graph, it is 35 at 0