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

Let's analyze the pattern in the table to find the equation that represents the relationship between $ y $ (the total cost) and $ x $ (the number of tickets).

The table shows:

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

### Step 1: Find the rate of change (slope)
Notice that as the number of tickets increases by 1, the total cost increases by 4. This means that the slope (or rate of change) is 4.

Thus, the equation has a form:
\[
y = 4x + b
\]
where $ b $ is the y-intercept.

### Step 2: Find the y-intercept
To find $ b $, use the point $ (x, y) = (1, 6) $. Substitute this into the equation $ y = 4x + b $:

\[
6 = 4(1) + b
\]
\[
6 = 4 + b
\]
\[
b = 2
\]

### Final Equation:
The equation that represents the relationship is:
\[
y = 4x + 2
\]

Thus, the correct answer is:
**C. $ y = 4x + 2 $**

Would you like further clarification or more details?

### Related Questions:
1. How do you calculate the slope from a table of values?
2. What does the y-intercept represent in real-world problems?
3. How can you check if a table of values represents a linear relationship?
4. Can you find the equation using two different points from the table?
5. How would the equation change if the slope were different?

**Tip**: When dealing with linear relationships, always look for how much the dependent variable (total cost) changes when the independent variable (number of tickets) increases by 1.

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

Find the linear equation representing the relationship between the number of tickets and the total cost. The problem uses the slope-intercept form to determine that the equation is y = 4x + 2. This solution is ideal for students in Grades 6-8, covering key algebraic concepts like slope and y-intercept.

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