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Let's analyze the question based on the information provided in the image.

We have two linear functions:

1. **Function A** is represented by a table of values:

| x   | y   |
| --- | --- |
| -9  | -1  |
| 3   | 3   |
| 9   | 5   |

2. **Function B** is given by the equation \( y = \frac{1}{3}x \).

### Step 1: Find the y-intercept of Function A

To find the y-intercept of Function A, we need to write its equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

First, let's calculate the slope \( m \) using two points from the table: (3, 3) and (9, 5).

The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{9 - 3} = \frac{2}{6} = \frac{1}{3}
\]
So, the slope \( m \) is \( \frac{1}{3} \).

Now, use the slope-intercept form \( y = mx + b \) and plug in one point, say (3, 3), to solve for \( b \):
\[
3 = \frac{1}{3}(3) + b \quad \Rightarrow \quad 3 = 1 + b \quad \Rightarrow \quad b = 2
\]
So, the equation of Function A is:
\[
y = \frac{1}{3}x + 2
\]
Thus, the y-intercept of Function A is \( 2 \).

### Step 2: Find the y-intercept of Function B

Function B is already given in the form \( y = \frac{1}{3}x \), which means the slope is \( \frac{1}{3} \) and the y-intercept is \( 0 \), because there is no constant term added.

### Step 3: Compare the y-intercepts

- The y-intercept of Function A is \( 2 \).
- The y-intercept of Function B is \( 0 \).

Clearly, the y-intercept of Function A is greater than the y-intercept of Function B.

### Answer:
The correct statement is:
- **The y-intercept of Function A is greater than the y-intercept of Function B.**

Would you like more details or have any questions?

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Here are 5 related questions for further practice:
1. How do you determine the slope of a line from a table of values?
2. What is the importance of the y-intercept in graphing a linear equation?
3. How can you graph Function A and Function B on the same plane to compare their y-intercepts visually?
4. How do different slopes affect the steepness of a line in linear functions?
5. Can two different linear functions have the same slope but different y-intercepts? What does that mean geometrically?

**Tip:** When dealing with linear equations, always check if they are in slope-intercept form \( y = mx + b \). It helps identify the slope and y-intercept quickly!

Which statement is true about the y-intercepts of Function A and Function B?

Learn how to compare the y-intercepts of Function A and Function B. Function A is given by a table of values, and Function B by the equation y = (1/3)x. Discover how to find y-intercepts and solve linear functions for Grades 7-9.

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