Question

It costs a family of two $25 to go to the state fair, and a family of six $65. Find the equation, rate of change, and initial value of the function that represents this situation?

Answer 1

rate of change is 10

initial value is 5

Equation of Function is y=10x+5

Explanation:

Answer 2

Explanation:

Given:

Family of 2

Cost, C1 = $25

Family of 6

Cost, C2 = $65

Given that 2 points are given above as the following in coordinate form:

A(2,25) and B(6,65)

Rate of change is given as = (y2 - y1)/(x2 - x1)

= (65 - 25)/(6-2)

= 40/4

Therefore,

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

(y - 25)/(65 - 25) = (x - 2)/(6 - 2)

(y - 25)/40 = (x - 2)/4

(y - 25) = 40/4 × (x - 2)

(y - 25) = 10 × (x - 2)

Expanding,

y - 25 = 10x - 20

y = 10x - 20 + 25

y = 10x + 5