Question

The linear function y=-0.6x + 31 models the percentage of men in a certain city, y, smoking cigarettes 2 years after 2000. Findthe 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 = -0.6(Enter: increased or decreased or not changed) byb) The value of the function decreasedper year after 2000.

Answer 1

From the statement, we know that the function for the percentage of men in a certain city smoking cigarette (y) is:

`y=-0.6x+31,`

where x is the independent variable, the number of years 2 years after 2000.

a) Because the model is given by a linear equation of the form:

`y=m\cdot x+b,`

where m is the slope and b the y-intercept. Comparing with the equation of the problem, we identify the value of the slope:

`m=-0.6.`

b) Because the slope of the function is negative, its value is -0.6, we know that the percentage of men that smokes cigarettes is decreasing, and the value decreases 0.6 per year. This is the interpretation of the slope in terms of the rate of change of male smokers in this city over time.