Question

Shira’s math test included a survey question asking how many hours students spent studying for the test.The scatterplot below shows the relationship between how many hours students spent studying and their score on the test.A line was fit to the data to model the relationship

Which of these linear questions best describes the given model?
A. y=x+45

B. y=10x+45

C. y=-10x+45

Based on this equation, estimate the score for a student that spent 5 hours studying.

Answer 1

A 1-hour increase in study time was associated with an average score change of 10 points

Explanation:

Got it right on Khan :)

Answer 2

Part 1) Option B.
`y=10x+45`

Part 2) The score is 95

Explanation:

Part 1) Linear equation that best describes the given model

Let

x ---> number of hours students spent studying

y ---> their score on the test

Looking at the line that was fit to the data to model the relationship

The slope is positive

The y-intercept is the point (0,45)

For x=1, y=55 ----> point (1,55)

Find the slope

The formula to calculate the slope between two points is equal to

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

substitute the points (0,45) and (1,55)

`m=(55-45)/(1-0)=10`

Find the equation of the line in slope intercept form

`y=mx+b`

we have

`m=10\\b=45`

substitute

`y=10x+45`

Part 2) Estimate the score for a student that spent 5 hours studying.

For x=5 hours

substitute in the linear equation and solve for y

`y=10(5)+45=95`