What is the slope and y intercept for the linear function f(x) =  1/3x

– 5.

For the linear function \( f(x) = \frac{1}{3}x - 5 \), the slope and y-intercept can be determined directly from the equation.

The general form of a linear equation is \( f(x) = mx + b \), where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

In your function \( f(x) = \frac{1}{3}x - 5 \):
- The slope \( m \) is \( \frac{1}{3} \).
- The y-intercept \( b \) is \( -5 \).

### Summary:
- **Slope**: \( \frac{1}{3} \)
- **Y-intercept**: \( -5 \)

Would you like further details or have any other questions? 

Here are 8 related questions to consider:
1. How do you find the x-intercept of the linear function \( f(x) = \frac{1}{3}x - 5 \)?
2. What is the equation of a line parallel to \( f(x) = \frac{1}{3}x - 5 \)?
3. How would the graph of \( f(x) = \frac{1}{3}x - 5 \) change if the slope were doubled?
4. What does the slope represent in the context of a real-world problem?
5. How do you convert a linear equation to slope-intercept form?
6. Can you express \( f(x) = \frac{1}{3}x - 5 \) in standard form?
7. What is the effect of changing the y-intercept in a linear function?
8. How do you determine the point where two linear functions intersect?

**Tip**: Always remember that the slope of a line represents the rate of change, while the y-intercept shows the point where the line crosses the y-axis.

Explore how to find the slope and y-intercept of linear functions with a detailed explanation of the function f(x) = (1/3)x - 5. This page covers fundamental algebraic concepts, including linear functions, slope, and y-intercept. Suitable for students in Grades 7-9.

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