Question

the data in the table compares x, the number of pages in a chapter, to y, the amount of time, in minutes, spent reading. the function y = 0.86x - 0.09 models the data in the table. which is the best prediction for the number of pages in a chapter that takes 18 minutes to read? 15 17 19 21 time spent reading pages in a chapter time spent reading (minutes) 10 8 12 11 5 4 26 22 20 17

Explanation:

Step1: Substitute y = 18 into the equation

We have the model \( y = 0.86x - 0.09 \), and we know \( y = 18 \). So we substitute \( y \) with 18 in the equation:
\( 18 = 0.86x - 0.09 \)

Step2: Solve for x

First, add 0.09 to both sides of the equation:
\( 18 + 0.09 = 0.86x \)
\( 18.09 = 0.86x \)

Then, divide both sides by 0.86 to solve for \( x \):
\( x=\frac{18.09}{0.86}\approx21 \) (Wait, no, wait, let's recalculate. Wait, 18.09 divided by 0.86: 0.86*21 = 18.06, which is close to 18.09. Wait, but maybe I made a mistake. Wait, the equation is y = 0.86x - 0.09. We need to find x when y = 18. So:

\( 18 = 0.86x - 0.09 \)

Add 0.09 to both sides:

\( 18 + 0.09 = 0.86x \)

\( 18.09 = 0.86x \)

Now, divide 18.09 by 0.86:

\( x=\frac{18.09}{0.86}\approx21 \)? Wait, but let's check the options. Wait, maybe I miscalculated. Wait, 0.86*21 = 18.06, which is very close to 18.09. But the options are 15,17,19,21. Wait, but let's check again. Wait, maybe the question is to find x when y=18. Let's do the calculation again:

\( 18 = 0.86x - 0.09 \)

\( 0.86x = 18 + 0.09 = 18.09 \)

\( x = 18.09 / 0.86 \approx 21 \). So the answer is 21? But wait, let's check the table. For x=20, y=17. So when y=18, x should be a bit more than 20. So 21 is the closest. Wait, but the options include 21. So the answer is 21.

Wait, but maybe I made a mistake. Wait, let's check the calculation again. 18.09 divided by 0.86: 0.8620 = 17.2, 0.8621=18.06, 0.86*21.03=18.09. So x≈21. So the best prediction is 21.

Answer:

21