Question

For a field trip, a bus company charges a flat fee of $70 plus an additional fee per student. For 25 students, the total cost is $132.50. If there are 30 students, the total cost is $145.00. Write an equation that represents the total cost y of the field trip for x students; y=mx+b.

Answer 1

The form of the linear equation is

y = m x + b, where

m is the slope (rate of change)

b is the y-intercept (initial amount)

Since x represents the number of students

y represents the cost of the trip

There is a flat fee of $70

Which means b = 70

The additional fee per student is m

To find m we have two points

25 students , cost = $132.50

30 students , cost = $145.00

So the points are (25, 132.50) and (30, 145.00)

We will use these points to find m

The rule of m = change of y/change of x

Change of y = 145.00 - 132.50 = 12.5

Change of x = 30 - 25 = 5

m = 12.5/5 = 2.5

Substitute values of b and m in the form of the equation

y = 2.5 x + 70

The equation that represents the total cost is

y = 2.5 x + 70