The table shows the cost of movie tickets based on the number of tickets purchased.

Question

Number of Tickets Cost
2
$17.00

3
$25.50

4
$34.00

5
$42.50

Based on this proportional relationship, find the constant of proportionality (r).
Using the value for r,
enter an equation that will calculate the cost (y)
of x
movie tickets in the form of y=rx.
Round to the nearest tenth.

Answer 1

To find the constant of proportionality (r) from the data provided, we can use the cost of the tickets divided by the number of tickets purchased.

Using the data provided, we can calculate r using the cost for a known number of tickets.

From the first row:

• For 2 tickets: \( r = \frac{17.00}{2} = 8.50 \)

From the second row:

• For 3 tickets: \( r = \frac{25.50}{3} = 8.50 \)

From the third row:

• For 4 tickets: \( r = \frac{34.00}{4} = 8.50 \)

From the fourth row:

• For 5 tickets: \( r = \frac{42.50}{5} = 8.50 \)

Since the value of r is consistent across all calculations, we conclude that the constant of proportionality is:

\[ r = 8.5 \]

Now, we can write the equation that calculates the cost (y) of x movie tickets in the form \( y = rx \):

\[ y = 8.5x \]

So, the final answer is:

• Constant of proportionality (r): 8.5
• Equation: \( y = 8.5x \)