$$  $$$$  $$$$ y=\log\frac13 $$$$ x $$Graph 

Here is the graph of the function $ y = \log\left(\frac{1}{3}\right) \cdot x $. As expected, the graph is a straight line with a negative slope, indicating that the function decreases as $ x $ increases.

Would you like more details on how the logarithm affects the slope, or do you have any other questions?

Here are 8 questions related to this concept:

1. What is the general effect of a negative logarithm on the slope of a line?
2. How would the graph change if the logarithm were positive?
3. What is the slope if the logarithm is $ \log(3) $ instead of $ \log\left(\frac{1}{3}\right) $?
4. How do you interpret the y-intercept in this context?
5. What happens to the graph if $ x $ is replaced with $ x^2 $?
6. How would the graph look if the function were $ y = \log\left(\frac{1}{3}\right) \cdot x + 2 $?
7. Can you explain how logarithms affect exponential functions?
8. How does changing the base of the logarithm affect the graph?

**Tip:** The slope of a line in the form $ y = mx $ can be directly affected by the base of the logarithm used. Different bases will yield different slopes.

Explore the graph of the function y = log(1/3) * x, a linear equation with a negative slope due to the logarithm. Understand how logarithms affect the slope of a line and interpret the graph's behavior. Suitable for students studying logarithmic functions in Grades 10-12.

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