5 Problems - SHOW ALL WORK!
1. What is the equation of the function shown by the graph? Show your work. Remember to find two integer points where the line passes through so you can calculate the slope. (Hint: One is (-4, 4) Find the second point)
2. Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase for different number of tickets in the table shown.
a. What is the equation that models this linear function? Show your work. Don’t forget to define your variables!
b. Use the phrase is a function of to describe the situation Tickets 2 3 6 Total Cost $32.00 $44.50 $82.00 represented by the equation you wrote in problem 3a.
c. How much is each movie ticket?
1. To find the equation of the function shown by the graph, we need to find the slope and the y-intercept. From the given point (-4, 4), we can choose another point on the line to calculate the slope. Let's choose the point (2, 0).
The formula for finding slope is (y2 - y1) / (x2 - x1). Plugging in the values, we get:
slope = (0 - 4) / (2 - (-4)) = -4 / 6 = -2/3
Now that we have the slope, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (-4, 4) and the slope -2/3, the equation becomes:
y - 4 = (-2/3)(x - (-4))
Simplifying further:
y - 4 = (-2/3)(x + 4)
y - 4 = (-2/3)x - 8/3
y = (-2/3)x + 4/3
So, the equation of the function shown by the graph is y = (-2/3)x + 4/3.
2. a. To find the equation that models this linear function, we need to find the slope and the y-intercept. From the given table, we can choose two points: (2, 32.00) and (6, 82.00).
The formula for finding slope is (y2 - y1) / (x2 - x1). Plugging in the values, we get:
slope = (82.00 - 32.00) / (6 - 2) = 50.00 / 4 = 12.50
Now that we have the slope, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (2, 32.00) and the slope 12.50, the equation becomes:
y - 32.00 = 12.50(x - 2)
Simplifying further:
y - 32.00 = 12.50x - 25.00
y = 12.50x + 7.00
So, the equation that models this linear function is y = 12.50x + 7.00.
b. The phrase "Total Cost is a function of Tickets" can be represented by the equation: Total Cost = 12.50x + 7.00, where x represents the number of tickets.
c. To find the cost of each movie ticket, we can look at the equation in problem 2b. Since the coefficient of x is 12.50, we can conclude that each movie ticket costs $12.50.