The table shows the total cost for different number of tickets.
 
Number of
Tickets	1
2
3
4
5
Total Cost ($)	6
10
14
18
22

Which equation represents the relationship between y
, the cost of x
tickets?
A.y=2x+4

B.y=4x

C.y=4x+2

D.y=4x−2


We can determine the correct equation by analyzing the given data.

### Number of Tickets (x) vs. Total Cost (y):

| Number of Tickets (x) | Total Cost (y) |
|-----------------------|----------------|
| 1                     | 6              |
| 2                     | 10             |
| 3                     | 14             |
| 4                     | 18             |
| 5                     | 22             |

1. **Step 1: Look for the pattern in the cost.**
   - The difference in total cost between consecutive tickets is constant.
   - $ 10 - 6 = 4 $, $ 14 - 10 = 4 $, $ 18 - 14 = 4 $, and $ 22 - 18 = 4 $.
   - So, the cost increases by $4 for each additional ticket.

2. **Step 2: Derive the equation form.**
   - This suggests the equation is linear with the slope $ m = 4 $.
   - So, we start with the equation $ y = 4x + b $, where $ b $ is the y-intercept.

3. **Step 3: Determine the y-intercept.**
   - When $ x = 1 $, $ y = 6 $.
   - Substitute $ x = 1 $ and $ y = 6 $ into the equation $ y = 4x + b $:
     \[
     6 = 4(1) + b \\
     6 = 4 + b \\
     b = 2
     \]
   - Therefore, the equation is $ y = 4x + 2 $.

4. **Step 4: Check the options.**
   - The correct equation is $ y = 4x + 2 $, which corresponds to **option C**.

### Final Answer: **C. $ y = 4x + 2 $**

Would you like more details or have any questions?

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Here are 5 related questions to expand on this:

1. What does the slope represent in this context?
2. How would the equation change if the ticket price increased by $5 per ticket instead of $4?
3. If you bought 10 tickets, what would the total cost be according to the equation?
4. How would you graph this equation on a coordinate plane?
5. What is the significance of the y-intercept in this problem?

**Tip:** When dealing with linear relationships, always check for a constant rate of change (slope) to derive the equation.

The table shows the total cost for different number of tickets.

Number of Tickets: 1, 2, 3, 4, 5
Total Cost ($): 6, 10, 14, 18, 22

Which equation represents the relationship between y, the cost of x tickets?
A. y=2x+4
B. y=4x
C. y=4x+2
D. y=4x−2

Learn how to determine the linear equation that represents the relationship between the number of tickets and total cost. This example uses real data, explores the slope-intercept form (y = mx + b), and is suitable for students in Grades 6-8.

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