A) Linear relationship
B) The model predicts score = 60 for t = 3 h
C) 45 is the test score when the time spent on homework is zero
Step-by-step explanation:
A)
The relationship between the number of hours spent on homework and the test score is a linear relationship.
In fact:
- The hours spent on homework is represented on x-axis
- The test score is represented on the y-axis
By looking at the points in the scatter plot, we observe that as the value of the x (number of hours spent on homework) increases, the value of y (test score) also increases; also we note that the points on the scatter plot are distributed approximately around a straight line, therefore we can say that the two variables have a linear relationship.
B)
The function used by Sally in order to model the relationship between the two variables is
[tex]y=5x+45[/tex]
where
x is the number of hours spent on homework
y is the test score
Here we want to evaluate the test score when the number of hours spent on homework is
x = 3 h
Therefore, substituting into the function, we get
[tex]y=5\cdot 3 + 45 = 15+45 = 60[/tex]
So, the model predicts a test score of 60 when the number of hours spent on homework is 3.
C)
We can now interpret the function used to model the relationship between the two variables:
[tex]y=5x+45[/tex]
By comparing it with the equation of a straight line:
[tex]y=mx+q[/tex]
where m is the slope and q the y-intercept, we infere that:
- 5 is the slope of the line --> in this context, it represents the increase in the test score per increase of hours spent on homework. In other words, it means that for every additional hour spent on homework, the score in the test increases by 5
- 45 is the y-intercept of the line --> in this context, it represents the test score when the number of hours spent on homework is zero.
Learn more about straight lines:
brainly.com/question/4152194
brainly.com/question/12941985
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