Answer:
![(a)\ c(x) = 39 + 0.09 x](https://tex.z-dn.net/?f=%28a%29%5C%20c%28x%29%20%3D%2039%20%2B%200.09%20x)
![(b)\ \$53.4](https://tex.z-dn.net/?f=%28b%29%5C%20%5C%2453.4)
Step-by-step explanation:
Given
![Base\ Charge = \$39](https://tex.z-dn.net/?f=Base%5C%20Charge%20%3D%20%5C%2439)
per mile
Solving (a): Linear Equation
The total charges (c(x)) is: the base charge + the rate * number of miles (x).
So, we have:
![c(x)= 39 + 0.09 * x](https://tex.z-dn.net/?f=c%28x%29%3D%2039%20%2B%200.09%20%2A%20x)
![c(x) = 39 + 0.09 x](https://tex.z-dn.net/?f=c%28x%29%20%3D%2039%20%2B%200.09%20x)
Solving (b): Cost of rent, if miles = 160
This implies that x = 160
So, we have:
![c(x) = 39 + 0.09 x](https://tex.z-dn.net/?f=c%28x%29%20%3D%2039%20%2B%200.09%20x)
![c(160) = 39 + 0.09 *160](https://tex.z-dn.net/?f=c%28160%29%20%3D%2039%20%2B%200.09%20%2A160)
![c(160) = 39 + 14.4](https://tex.z-dn.net/?f=c%28160%29%20%3D%2039%20%2B%2014.4)
![c(160) = 53.4](https://tex.z-dn.net/?f=c%28160%29%20%3D%2053.4)
1.3y +3.2 = 1.3y +3.2
we notice that both sides of the equation are identical. So substitute y with any value and the equation would still be correct.
y has infinite solutions.