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
tickets cost
2 $32
3 $44.50
6 $82
What is the equation that models this linear function? Show your work. Don’t forget to define your variables!
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.
How much is each movie ticket?
To find the equation that models the linear function, we need to find the slope and the y-intercept.
We are given two points that the line passes through: (-4, 4) and (2, 32).
The slope is calculated using the formula: slope = (y2 - y1) / (x2 - x1)
Using the two points, we can calculate the slope as: slope = (32 - 4) / (2 - (-4)) = 28 / 6 = 14/3
Let's assume 'x' represents the number of tickets, and 'y' represents the total cost.
Now, we have the slope 'm' as 14/3 and we have a point (2, 32).
Using the point-slope form of a linear equation: y - y1 = m(x - x1)
Plugging in the values, we get: y - 32 = (14/3)(x - 2)
Simplifying the equation, we get: y - 32 = (14/3)x - 28/3
Adding 32 to both sides to isolate 'y', we get: y = (14/3)x - 28/3 + 32
Simplifying further, we get the equation: y = (14/3)x + 4/3
So, the equation that models this linear function is: y = (14/3)x + 4/3.
The phrase "Total Cost is a function of Tickets" describes the situation represented by the equation we wrote.
To find out how much each movie ticket costs, we can look at the y-intercept of the equation. The y-intercept represents the cost when the number of tickets is 0.
From the equation y = (14/3)x + 4/3, we can see that when x = 0, y = 4/3.
Therefore, each movie ticket costs $4/3, or approximately $1.33.