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.

Explanation:

Let us take two points

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

Using the two-point formula,

$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

On substitution we get,

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

Thus, the linear equation is,

$y=\frac{35}{8}x+\frac{1955}{4}$

Therefore, for a 54-hour review course

The average score is,

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

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