Question

Create the required linear function an use it to answer the question.Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on thatexam. Persons taking a 70-hour review course average a score of 795. Based on these two data points, create alinear equation for the function that describes how score varies as a function of time. Use this function topredict an average score for persons taking a 54-hour review course. Round your answer to the tenths place.

Answer 1

Given:

For a 30-hour review course, the average score is 620.

For a 70-hour review course, the average score is 795.

To find: The linear equation and the average score for 54 hours review course.

Step-by-step explanation:

Let us take two points

`(30,620)\text{ and }(70,795)`

Using the two-point formula,

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

On substitution we get,

`\begin{gathered} (y-620)/(795-620)=(x-30)/(70-30) \\ (y-620)/(175)=(x-30)/(40) \\ 40y-24800=175x-5250 \\ 40y=175x-5250+24800 \\ 40y=175x+19550 \\ y=(35)/(8)x+(1955)/(4) \end{gathered}`

Thus, the linear equation is,

`y=(35)/(8)x+(1955)/(4)`

Therefore, for a 54-hour review course

The average score is,

`\begin{gathered} y=(35)/(8)(54)+(1955)/(4) \\ y=725 \end{gathered}`

Thus, the average score for a 54-hour review course is 725.