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