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The scatter plot shows students scores for quiz 1 and quiz 2. a. What is the quiz 1 score for a student who earned a score of 13 on quiz 2? b. Did any student(s) earn the same score on both quiz 1 and quiz 2? Explain. c. The dotted line shows the line of best fit. Write its equation and then interpret the meaning of the slope and y-intercept. Does the y-intercept make sense in the context of the problem? The slope should be represented as a fraction or whole number just to let you know. Here is a picture attached of the graph.

The scatter plot shows students scores for quiz 1 and quiz 2. a. What is the quiz-example-1
User Norbert Hartl
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1 Answer

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b) Looking at the graph, the scores of quiz 2 are on the y axis while the scores of quiz 1 are on the y axis. Each samll box on both axes is 2 units. This means that half of a samll box is 1 unit. We can locate a score of 15 in quiz 2(halfway between 14 and 16). It also corresponds to a score of 15 in quiz 1. Thus, 1 student earned 15 marks in quiz 1 and 2

c) The equation of the line of best fit is written in the slope intercept form which is expressed as

y = mx + b

where

m = slope

b = y intercept

We would calculate the slope by applying the formula,

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

where

y1 and y2 are y coordinates of initial and final points on the line.

x1 and x2 are x coordinates of initial and final points on the line.

Picking points on the graph, we have

when x1 = 10, y1 = 8

when x2 = 16, y2 = 14

By substituting these values into the formula,

m = (14 - 8)/(16 - 10) = 6/6 = 1

We would find the y intercept by substituting m = 1, x = 10 and y = 8 into the slope intercept equation. We have

8 = 1 * 10 + b = 10 + b

b = 8 - 10

b = - 2

Substituting m = 1 and b = - 2 into the slope intercept equation, the equation of the line of best fit is

y = x - 2

The slope is 1 and since it is small, it tells us that for each score of 1 that a student gets in quiz 2, he would likely get a score of 1 in quiz 1.

Since the y intercept is negative, it doesn't make sense in the concept of the problem because a student cannot earn a negative score in any of the quizzes. The y intercept tells us that the student earned - 2 in quiz 2 and 0 in quiz 1

User Abdul Azeez
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