Answer:
Part 1) [tex]y=32.5x+11.95[/tex]
Par 2) see the explanation
Part 3) [tex]\$401.95[/tex]
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
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept (one-time processing fee)
In this problem we have
[tex]b=\$11.95[/tex]
ordered pairs (4,141.95) and (7,239.45)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values in the formula
[tex]m=\frac{239.45-141.95}{7-4}[/tex]
[tex]m=\frac{97.5}{3}[/tex]
[tex]m=32.5[/tex]
substitute the values in the linear equation
[tex]y=32.5x+11.95[/tex]
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
[tex]m=\$32.5\ per\ ticket[/tex]
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
[tex]b=\$11.95[/tex]
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
[tex]y=32.5(12)+11.95[/tex]
[tex]y=\$401.95[/tex]
