Answer:
Part 1) ![y=32.5x+11.95](https://tex.z-dn.net/?f=y%3D32.5x%2B11.95)
Par 2) see the explanation
Part 3) ![\$401.95](https://tex.z-dn.net/?f=%5C%24401.95)
Step-by-step explanation:
Part 1) Write an equation in slope intercept form to represent this problem
Let
x ----> the number of tickets
y ---> the total cost
The linear equation in slope intercept form is equal to
where
m is the slope or unit rate
b is the y-intercept (one-time processing fee)
In this problem we have
![b=\$11.95](https://tex.z-dn.net/?f=b%3D%5C%2411.95)
ordered pairs (4,141.95) and (7,239.45)
Find the slope
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
substitute the values in the formula
![m=\frac{239.45-141.95}{7-4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B239.45-141.95%7D%7B7-4%7D)
![m=\frac{97.5}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B97.5%7D%7B3%7D)
![m=32.5](https://tex.z-dn.net/?f=m%3D32.5)
substitute the values in the linear equation
![y=32.5x+11.95](https://tex.z-dn.net/?f=y%3D32.5x%2B11.95)
Part 2) What does your slope represent in this problem? What does your y-intercept represent in this problem?
a) The slope of the linear equation represent the unit rate, so the slope represents the cost of one ticket
![m=\$32.5\ per\ ticket](https://tex.z-dn.net/?f=m%3D%5C%2432.5%5C%20per%5C%20ticket)
b) The y-intercept is the value of y when the value of x is equal to zero
In this context, the y-intercept represent the one-time processing fee
![b=\$11.95](https://tex.z-dn.net/?f=b%3D%5C%2411.95)
Part 3) Use the equation to find how much Alan would have to pay for 12 tickets
For x=12 tickets
substitute in the linear equation
![y=32.5(12)+11.95](https://tex.z-dn.net/?f=y%3D32.5%2812%29%2B11.95)
![y=\$401.95](https://tex.z-dn.net/?f=y%3D%5C%24401.95)