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.