Question

The linear function y = -0.3x + 26 models the percentage of men in a certain city,

y, smoking cigarettes 3 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.

Answer 1

The slope of the linear function is -0.3, indicating a negative rate of change in the percentage of male smokers over time.

Step-by-step explanation:

The slope of a linear function represents the rate of change between the independent and dependent variables. In this case, the slope of the function y = -0.3x + 26 is -0.3. This means that for every one-unit increase in the independent variable (years after 2000), the percentage of men smoking cigarettes in the city decreases by 0.3%.

So, the slope of -0.3 indicates a negative rate of change. As time progresses, the percentage of male smokers in the city decreases. For example, if we increase the number of years after 2000 by 1, the percentage of male smokers would decrease by 0.3%.

In summary, the slope of the model represents the rate at which the percentage of male smokers decreases over time in this city.