y = 10x + 5 is the required equation.
<u>Explanation:</u>
A family of two to go to state fair is $25
A family of six to go to state fair is $65
So the 2 points are (2,25) and (6,65)
Rate of change = (y2-y1)/ (x2-x1)
Plugin the values, we will get,
= (65 - 25)/ (6-2)= 40/4 = 10
Equation can be written as,
(y - y₁) / (y₂ - y₁) = (x-x₁)/(x₂-x₁)
(y-25)/(65-25) = (x-2)/(6-2)
(y-25)/ 40 = (x-2) / 4
4(y-25) = 40(x-2)
4y - 100 = 40x - 80
4y = 40x - 80 + 100
4y = 40x + 20
Dividing the equation by 4, we will get,
y = 10x + 5 is the equation required.
