Respuesta :
Required function y = 2x + 40 to represents linear relationship between number of people and total cost shows following statements are true:
a. Independent variable represents the number of people.
b. Initial value for the picnic is $40.
d. Cost of the picnic increases as per the number of people.
As given in the question,
Let 'x' represents the number of people
And 'y' represents the total cost
Linear relationship between number of people and total cost is:
y = mx + b
Consider two points (x₁ , y₁) = (6, 52) and ( x₂ , y₂ ) = ( 9 , 58)
Slope 'm' = ( y₂ - y₁)/ (x₂ - x₁)
= (58 - 52)/ (9 -6)
= 6 / 3
= 2
y = 2x + b
Now for, (x. y) = ( 12,64)
64 = 2(12) +b
⇒b = 64 - 24
⇒b = 40
Hence, required function is :
y = 2x + 40
a. Independent variable is the number of people.
Here it is x which represents the number of people.
True.
b. Initial value for the picnic is $40
y- intercept when x =0 ⇒ y = $40
True.
c. Rate of change is $8.67 per person.
No, rate of change is $2 per person.
d. Number of people increases as total cost of picnic increases
True .
e. If x = 4
⇒y = 2(4) + 40
= 48 ≠46
False.
Therefore, function y = 2x + 40 represents that following statements are true:
a. Independent variable represents the number of people.
b. Initial value for the picnic is $40.
d. Cost of the picnic increases as per the number of people.
The above question is incomplete, the complete question :
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. a. The independent variable is the number of people.
b. The initial value (initial fee) for the picnic is $40.
c. The rate of change is $8.67 per person.
d. As the number of people increases, the total cost of the picnic increases.
e. If 4 people attended the picnic, the total cost would be $46.
Number of people Total cost ($)
6 52
9 58
12 64
15 70
Learn more about function here
brainly.com/question/12426369
#SPJ4
