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:

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?

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!