The function you provided is:

\[
f(x) = \frac{1}{3}x - 7
\]

This is a linear function, and its general form is:

\[
f(x) = mx + b
\]

Where:
- \( m = \frac{1}{3} \) is the slope of the line.
- \( b = -7 \) is the y-intercept, which is the point where the line crosses the y-axis (at \( x = 0 \)).

### Key characteristics:
1. **Slope** (\( m \)): This represents the rate of change. In this case, for every 1 unit increase in \( x \), the value of \( f(x) \) increases by \( \frac{1}{3} \).
   
2. **Y-intercept** (\( b \)): The function crosses the y-axis at \( y = -7 \).

If you graph this function, it will be a straight line with a gradual upward slope (since \( \frac{1}{3} \) is positive and less than 1, the rise is slow).

Would you like details on graphing this, finding specific values, or applying the function?

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Here are 5 related questions you might find helpful:
1. What are the coordinates of the point where the line crosses the x-axis?
2. How do you calculate the value of \( f(x) \) for specific \( x \) values?
3. What is the slope of the line and what does it represent geometrically?
4. How do you determine if two linear functions are parallel or perpendicular?
5. What changes to the function would make the line steeper or flatter?

**Tip:** When working with linear functions, the slope determines the direction and steepness of the line, while the intercept tells you where the line starts on the y-axis.

Explore the linear function f(x) = 1/3x - 7 with a detailed explanation of its slope and y-intercept. Learn how to graph this function, calculate values, and understand the relationship between slope and intercept. This problem is ideal for students in Grades 8-10 studying linear functions.

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