Question

mrs. thompson’s reading class is trying to read 900 total pages in a week. the scatterplot below shows the total minutes they have spent reading, and the number of pages they have left to read. use the scatterplot to answer questions 1-3.
1 the equation of the trend line shown is $p = -\frac{20}{9}m + 900$. use the trend line to predict the number of minutes it will take mrs. thompson’s class to complete the 900 pages.
2 which statement below accurately describes the relationship represented on the graph?
a the more minutes the students spend reading, the more pages they have left to read.
b the more pages the students have read, the faster they read.
c the more pages the students have left to read, the slower the students read.
d the more minutes the students spend reading, the less pages they have left to read.
3 what type of association is shown in the graph?
a positive association
b negative association
c nonlinear association
d no association

Explanation:

Question 1

Step1: Understand the goal

We need to find the number of minutes when the pages left \( p = 0 \) (since they complete 900 pages, pages left is 0). The trend line equation is \( p=-\frac{20}{9}m + 900 \).

Step2: Set \( p = 0 \) and solve for \( m \)

Set \( p = 0 \) in the equation:

$$ 0=-\frac{20}{9}m + 900 $$

Add \( \frac{20}{9}m \) to both sides:

$$ \frac{20}{9}m=900 $$

Multiply both sides by \( \frac{9}{20} \):

$$ m = 900\times\frac{9}{20}=\frac{8100}{20} = 405 $$

• Option A: As minutes increase, pages left should decrease (since they read more), so A is wrong.
• Option B: The graph shows a linear relationship (trend line) about time and pages left, not about reading speed with pages read. So B is wrong.
• Option C: The graph's trend is about time and pages left, not pages left and reading speed. So C is wrong.
• Option D: As minutes spent reading (x - axis) increase, pages left (y - axis) decrease, which matches D.

• Positive association: As one variable increases, the other increases. Here, as minutes (x) increase, pages left (y) decrease, so not positive.
• Negative association: As one variable increases, the other decreases. This matches the graph (more minutes, less pages left).
• Non - linear association: The trend line is linear, so not non - linear.
• No association: There is a clear trend, so not no association.

Answer:

405 minutes

Question 2