The plot shown below describes the relationship between students' scores on the first exam in a class and their corresponding scores on the second exam in the class. A line was fit to the data to model the relationship.

Which of these linear equations best describes the given model?

Choose 1 answer:
(A) $\hat{y}=2 x+10$
(B) $\hat{y}=x+10$
(c) $\hat{y}=2 x$
(D) $\hat{y}=x$

Based on this equation, estimate the score on the second exam for a student whose first exam score was 88 .
$\square$

Question

The plot shown below describes the relationship between students' scores on the first exam in a class and their corresponding scores on the second exam in the class. A line was fit to the data to model the relationship.

Which of these linear equations best describes the given model?

Choose 1 answer:
(A) $\hat{y}=2 x+10$
(B) $\hat{y}=x+10$
(c) $\hat{y}=2 x$
(D) $\hat{y}=x$

Based on this equation, estimate the score on the second exam for a student whose first exam score was 88 .
$\square$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine which linear equation best describes the given model, we need to compare the line of best fit in the scatter plot with the given equations. The line of best fit appears to pass through points around (20, 30) and (70, 80). ‖ ‖ step 2 ⋮ Let's test the given equations with these points. For (20, 30): - For $ \hat{y} = 2x + 10 $: $ \hat{y} = 2(20) + 10 = 40 + 10 = 50 $ (not a match) - For $ \hat{y} = x + 10 $: $ \hat{y} = 20 + 10 = 30 $ (match) - For $ \hat{y} = 2x $: $ \hat{y} = 2(20) = 40 $ (not a match) - For $ \hat{y} = x $: $ \hat{y} = 20 $ (not a match) ‖ ‖ step 3 ⋮ Now, let's test the point (70, 80): - For $ \hat{y} = 2x + 10 $: $ \hat{y} = 2(70) + 10 = 140 + 10 = 150 $ (not a match) - For $ \hat{y} = x + 10 $: $ \hat{y} = 70 + 10 = 80 $ (match) - For $ \hat{y} = 2x $: $ \hat{y} = 2(70) = 140 $ (not a match) - For $ \hat{y} = x $: $ \hat{y} = 70 $ (not a match) ‖ ‖ step 4 ⋮ Based on the points tested, the equation $ \hat{y} = x + 10 $ fits both points. ‖ ***B*** ‖ step 5 ⋮ To estimate the score on the second exam for a student whose first exam score was 88 using the equation $ \hat{y} = x + 10 $: $ \hat{y} = 88 + 10 = 98 $ ‖ ∻Answer∻ ∻Key Concept∻ ⚹Line of Best Fit⚹ ∻Explanation∻ ⚹The line of best fit is a straight line that best represents the data on a scatter plot. It can be used to make predictions based on the linear relationship between the variables.⚹◊What is the formula for calculating the predicted score on the second exam based on the given linear equation⍭ Generate me a similar question◊

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