At the local movie theater it costs $10.00 for 2 students to see a movie. It costs $15.00 for 3 students, and it costs $20.00 for 4 students. Let the number of students be the input. What is the function rule that relates the number of students to the cost of tickets?
y = 5x
To find the function rule that relates the number of students to the cost of tickets, we can create a table of values for the given data:
Number of Students (x) Cost of Tickets (y)
--------------------- -------------------
2 $10.00
3 $15.00
4 $20.00
We can observe that as the number of students increases by 1, the cost of tickets increases by $5. This shows a constant rate of change.
To find the function rule, we can use the slope-intercept form of a linear equation, y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
Using the values from our table, we can determine the slope (m) and y-intercept (b).
Let's take two points: (2, 10) and (3, 15).
Slope (m) = (y2 - y1) / (x2 - x1)
= (15 - 10) / (3 - 2)
= 5 / 1
= 5
Now let's use the point (2, 10) to find the y-intercept (b).
Using the slope-intercept form, we have:
10 = 5(2) + b
10 = 10 + b
b = 10 - 10
b = 0
Therefore, the function rule that relates the number of students (x) to the cost of tickets (y) is:
y = 5x + 0
Simplifying, the function rule is:
y = 5x
So, the cost of tickets is 5 times the number of students.
To find the function rule that relates the number of students to the cost of tickets, we need to analyze the given information.
From the given data, we can see that as the number of students increases, the cost of tickets also increases. Additionally, the cost of tickets depends on the number of students, so we can assume that this is a linear relationship.
Let's break down the given data:
- For 2 students, the cost is $10.00.
- For 3 students, the cost is $15.00.
- For 4 students, the cost is $20.00.
Based on this information, we can find the difference in cost as the number of students increases.
The difference in cost between 2 and 3 students is $15.00 - $10.00 = $5.00.
The difference in cost between 3 and 4 students is $20.00 - $15.00 = $5.00.
Since the difference is consistent ($5.00), we can conclude that the cost increases by $5.00 for each additional student.
Now, let's express this relationship in the form of a function rule.
Let C represent the cost of tickets and N represent the number of students.
We can write the function rule as:
C = 5N + b
To find the value of b (the y-intercept), we can substitute the values of C and N from any of the given data points. Let's use the data point with 2 students and $10.00 cost:
10 = 5(2) + b
10 = 10 + b
b = 10 - 10
b = 0
Therefore, the function rule that relates the number of students (N) to the cost of tickets (C) is:
C = 5N + 0, which simplifies to C = 5N.
So, the function rule is C = 5N.