Question

Let x=0 correspond to the year 2000. Approximate a linear function f(x)=ax+b for the smoking rate (as a percentage) using the points (6,21) and (15,16) The function is f(x)=□ (Use integers or decimals for any numbers in the expression. Round to the nearest tenth as needed.)

Answer 1

The estimated linear function for the smoking rate based on the points (6,21) and (15,16) is f(x) = -0.6x + 24.6.

Step-by-step explanation:

To approximate a linear function f(x) = ax + b for the smoking rate using the points (6,21) and (15,16), first, we need to determine the slope (a) of the line that passes through these points. The slope is calculated by the difference in the y-values divided by the difference in the x-values:

m = (y2 - y1) / (x2 - x1)

Substituting the given points:

m = (16 - 21) / (15 - 6) = -5 / 9

So the slope of the line, a, is approximately -0.6 (rounded to the nearest tenth).

Next, we need to find the y-intercept, b, of the line. We can use one of the points and the slope to solve for b:

y = ax + b

Using point (6,21):

21 = (-0.6)(6) + b

21 = -3.6 + b

b = 21 + 3.6 = 24.6

Therefore the estimated linear function is:

f(x) = -0.6x + 24.6