
The linear function y = -0.6x + 30 models the percentage of men in a certain city, y, smoking cigarettes x years after
2000. Find the slope for the model. Then describe what this means in terms of the rate of change of male smokers in this city over time.
a) m =
b) The value of the function
(Enter: increased or decreased or not changed) by
per year after 2000.


Let's break this down:

The given linear function is:  
\[ y = -0.6x + 30 \]

This is a linear equation in the slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

### a) The slope \( m \)
In the equation \( y = -0.6x + 30 \), the slope \( m = -0.6 \).

### b) Interpretation of the slope
The slope represents the rate of change in the percentage of male smokers per year. Since the slope is negative, it indicates that the percentage of male smokers is **decreasing** over time.

For each additional year after 2000, the percentage of male smokers decreases by 0.6%.

So, we can fill in the blanks:

### a) \( m = -0.6 \)

### b) The value of the function **decreased** by **0.6** per year after 2000.

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Would you like more details or have any other questions?

Here are 5 related questions for further exploration:
1. How would you interpret the y-intercept \( b = 30 \) in this context?
2. What will be the percentage of male smokers in 2010 according to this model?
3. In what year will the percentage of male smokers reach zero, according to this model?
4. How would the graph of this linear function look like, and what does it tell you about the trend?
5. What is the significance of a negative slope in linear models for real-life scenarios?

**Tip**: The slope tells us how quickly something is changing over time, and the sign of the slope (positive or negative) determines whether that change is an increase or decrease.

The linear function y = -0.6x + 30 models the percentage of men in a certain city, y, smoking cigarettes x years after 2000. Find the slope for the model. Then describe what this means in terms of the rate of change of male smokers in this city over time.
a) m = 
b) The value of the function (Enter: increased or decreased or not changed) by per year after 2000.

Learn how to interpret the slope of the linear function y = -0.6x + 30, which models the percentage of male smokers over time. Discover how the negative slope represents a 0.6% decrease in male smokers per year after 2000. Ideal for students in Grades 8-10.

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