a We are asked to determine the processing fee and write a linear equation to represent the total cost C for t tickets. Each ticket costs $52. Also, we know that Jackson ordered 5 tickets and the cost was $275. Let's start by determining the processing fee and linear equation that represents the total cost C. We can model it with a linear equation.
C=mt+b
In this form the cost C increases with the number of tickets t bought. In this case, the y-intercept is represented by the processing fee, which is fixed. We do not know this fee yet, but we do know that each extra ticket costs $52. So far, we can substitute m=52 into our equation.
C=52x+b
We also know that 5 tickets cost $275. By substituting (5,275) into the equation and solving for b we can determine the processing fee.
b Let's make a table of values for t=3,t=4, and t=7.
t
52t+15
C
3
52(3)+15
171
4
52(4)+15
223
7
52(7)+15
379
c To graph the equation, we plot the three points found in Part B and connect them with a straight line. Note that we neither have a negative number of tickets bought nor a negative cost, so our graph cannot take negative values.
To predict the cost of 8 tickets, we start at t=8 on the horizontal axis and go up until we hit the graph. After having hit the graph, we can determine the corresponding cost on the vertical axis.
It looks like the cost is around $420 and $440. In other words, about $430.
The equation we get in Part A can help us to find a more exact value.
C=52t+15
From the equation, we can see that the slope is 52. A slope of 52 means that for every 1 horizontal step in the positive direction, we take 52 vertical steps in the positive direction. We know that the line passes through (7,379). By adding 52 to 379 we can predict the value of 8 tickets.
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