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?

The table shows the relationship between the number of tickets (x) and the total cost (y) for each quantity. Let's examine the pattern:

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

### Step 1: Identify the pattern
Looking at the differences between consecutive costs:
- From 6 to 10, the difference is 4.
- From 10 to 14, the difference is 4.
- From 14 to 18, the difference is 4.
- From 18 to 22, the difference is 4.

This consistent difference of 4 suggests that the relationship is **linear**.

### Step 2: Express the relationship in equation form
The general form of a linear equation is:

\[
y = mx + b
\]

Where:
- $m$ is the slope (rate of change),
- $b$ is the y-intercept (the value of $y$ when $x = 0$).

We know the slope $m$ is 4 because the cost increases by 4 for each additional ticket.

### Step 3: Find the y-intercept
Substitute a known pair of values for $x$ and $y$ (such as $x = 1, y = 6$) into the equation to solve for $b$:

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

### Step 4: Write the final equation
Now that we know $m = 4$ and $b = 2$, the equation representing the relationship is:

\[
y = 4x + 2
\]

This equation shows that the cost of $x$ tickets is $4 per ticket, with an additional base cost of $2.

Would you like more details or have any questions?

### Related Questions:
1. How can you verify if the equation works for all points in the table?
2. What does the slope of 4 represent in real-world terms?
3. How would the equation change if the base cost increased?
4. Can you derive the equation if given a different table with changing slopes?
5. How do you interpret the y-intercept in the context of this problem?

### Tip:
Always check a few points from your data against your equation to verify its accuracy.

The table shows the total cost for different number of tickets. Which equation represents the relationship between y, the cost of x tickets?

Explore how to derive the linear equation y = 4x + 2, representing the total cost of tickets with a fixed price per ticket and a base cost. This problem helps students in Grades 6-8 understand linear equations, slope, and y-intercept using real-world examples.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation