The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. Which statements about the function described by the table are true? Check all that apply. The independent variable is the number of people. The initial value (initial fee) for the picnic is $40. The rate of change is $8.67 per person. As the number of people increases, the total cost of the picnic increases. If 4 people attended the picnic, the total cost would be $46.

We are given a set of value in a table form that shows the linear relationship between the number of people at a picnic and the total cost of the picnic as:

Number of people Total cost($)

6 52

9 58

12 64

15 70

So as the total cost depend on the number of people at the picnic.

Hence, the number of people will act as a independent variable and the total cost will represent the dependent variable.

Now as the table shows the linear relationship.

Hence we will find out the function that represent the total cost in terms of the number of people with the help of two values.

Let f(n) represents the cost of n people.

As the linear function pass through (6,52) and (9,58).

Hence, the function is given by:

[tex]f(n)-52=\dfrac{58-52}{9-6}\times (n-6)\\\\f(n)-52=\dfrac{6}{3}\times (n-6)\\\\f(n)-52=2(n-6)\\\\f(n)-52=2n-12\\\\f(n)=2n-12+52\\\\f(n)=2n+40[/tex]

Hence, the initial value for the picnic is the cost of the function f(n) when n=0

Hence when n=0 we have:

f(0)=40

Hence, initial cost is $ 40.

The rate of change is the slope of the linear function so by looking at the function we see that the rate of change is $ 2.

( Since, f(n)=2n+40 )

Clearly from the set of values we see that as the number of people increases the total cost of the picnic also increases.
If 4 people attend the picnic i.e. n=4

The cost of picnic is calculated as:

f(4)=2×4+40

f(4)=8+40

f(4)=48

Hence, total cost for 4 people is: $ 48.

facundo3141592 facundo3141592 · Answer 2 · 2021-10-26T16:47:24+02:00

We want to study the given linear equation by analyzing the points on the table.

The correct statements are:

a) The independent variable is the number of people.

b) The initial value (initial fee) for the picnic is $40.

d) As the number of people increases, the total cost of the picnic increases.

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by the formula:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Now let's analyze the table:

The x-values are the ones in the left and the y-values are the ones on the right, now from the table we can use two points, let's use the first two:

(6, 52) and (9, 58).

Then the slope is:

[tex]a = \frac{58 - 52}{9 - 3} = 2[/tex]

Then the line is something like:

y = 2*x + b

To find the value of b, we use the point (6, 52). This means that when x = 6, y must be equal to 52.

We will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b = 40

Then the linear equation is:

y = 2*x + 40

Now let's see which statements are correct.

a) The independent variable is the number of people.

True, the "x" represents the number of people.

b) The initial value (initial fee) for the picnic is $40.

True, the y-intercept does not depend on the value of x, so we can say that you need to pay that indifferent of the number of people that goes.

c)The rate of change is $8.67 per person.

False, the rate of change is equal to the slope, in this case is $2 per person.

d) As the number of people increases, the total cost of the picnic increases.

True.

e) If 4 people attended the picnic, the total cost would be $46.

To see if this is true or not, we just need to evaluate the function that we got in x = 4.

y = 2*4 + 40 = 48

So we can see that this is false.

If you want to learn more, you can read:

https://brainly.com/question/11897796