Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $52 for 180 miles. On another day she rented a car from the same agency and paid $77.50 for 350 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges. f(x) =

9514 1404 393

  f(x) = 0.15x +25

Step-by-step explanation:

We are given two points:

  (x, y) = (180, 52) or (350, 77.50)

The slope is given by ...

  m = (y2 -y1)/(x2 -x1)

  m = (77.50 -52)/(350 -180) = 25.50/170 = 0.15

The y-intercept is given by ...

  b = y -mx

  b = 52 -0.15×180 = 25

Then the equation for the linear function is ...

  f(x) = mx +b

  f(x) = 0.15x +25

its 50 miles away from the starting point