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

3b. 
How much will 7
 tickets cost?
A.$20

B.$30​​​​​​​

C.$28

D.$26



Let's analyze the given dataLet's analyze the given 

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

### Step 1: Find the pattern in the cost
Notice that the total cost increases by 4 dollars for each additional ticket:
- From 6 to 10: Increase of 4
- From 10 to 14: Increase of 4
- From 14 to 18: Increase of 4
- From 18 to 22: Increase of 4

This indicates that the slope (rate of change) is 4. So, the equation has the form:
\[
y = 4x + b
\]
where $ b $ is the y-intercept.

### Step 2: Find the y-intercept
Substitute $ x = 1 $ and $ y = 6 $ into the equation:
\[
6 = 4(1) + b
\]
\[
6 = 4 + b
\]
\[
b = 2
\]

Thus, the equation representing the relationship is:
\[
y = 4x + 2
\]

The correct answer is:
**C. $ y = 4x + 2 $**

### Step 3: Calculate the cost for 7 tickets
Using the equation $ y = 4x + 2 $, substitute $ x = 7 $:
\[
y = 4(7) + 2
\]
\[
y = 28 + 2
\]
\[
y = 30
\]

Therefore, the cost for 7 tickets is:
**B. $30**

---

Would you like more details or have any questions? Here are 5 related questions to consider:

1. What would the equation be if the cost increased by $5 for each additional ticket?
2. How would the equation change if the starting cost was $8 for 1 ticket?
3. Can you find the equation if the cost for 1 ticket was $10 and increased by $3 for each additional ticket?
4. What would the total cost be for 10 tickets using the equation $ y = 4x + 2 $?
5. How does the slope affect the rate of increase in the total cost?

**Tip:** When you notice a constant increase or decrease in a table, it often indicates a linear relationship between the variables.

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

How much will 7 tickets cost?
A.$20
B.$30
C.$28
D.$26

Learn how to find the linear equation that represents the relationship between the number of tickets and the total cost. The table provided shows ticket costs for 1 to 5 tickets. The solution involves the slope-intercept form of a linear equation. Suitable for students in Grades 6-8.

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