Question

Shira's math test included a survey question asking how many hours students spent studying for the test. The scatter plot 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 equations best describes the given model? Choose 1 answer: Choose 1 answer: (Choice A) A \hat y=x+45 y ^ ​ =x+45y, with, hat, on top, equals, x, plus, 45 (Choice B) B \hat y=10x+45 y ^ ​ =10x+45y, with, hat, on top, equals, 10, x, plus, 45 (Choice C) C \hat y=-10x+45 y ^ ​ =−10x+45y, with, hat, on top, equals, minus, 10, x, plus, 45 Based on this equation, estimate the score for a student that spent 555 hours studying.

Answer 1

Answer:

Part 1)  y=10x+45

Part 2) The score is 95

Step-by-step 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

$m=\frac{y2-y1}{x2-x1}$

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

$m=\frac{55-45}{1-0}=10$

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

y = 95