Q. 19 - Precalculus Enhanced with Graphing Utilities

Question

Video Games and Grade-Point Average Professor Grant Alexander wanted to find a linear model that relates the

number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

(a) Explain why the number of hours spent playing video games is the independent variable and cumulative grade-point average is the dependent variable.

(b) Use a graphing utility to draw a scatter diagram.

(c) Use a graphing utility to find the line of best fit that models the relation between the number of hours of video game playing each week and grade-point average. Express the model using function notation.

(d) Interpret the slope.

(e) Predict the grade-point average of a student who plays video games for 8 hours each week.

(f) How many hours of video game playing do you think a student plays whose grade-point average is 2.40?

Step-by-Step Solution

Answer

(a). Because the cumulative grade-point average is dependent on the number of hours spent playing video games.

(b).The scatter diagram is

(c) The  best fit line graph and the model using function notation is y = -0.094185x + 3.276344

(d). The slope is  -0.094185 

(e). The grade-point average of a student who plays video games for 8 hours each week is 2.31 and 2.54

(f). For 9.30449 hours of video game playing a student plays whose grade-point average is 2.40

Step 1. Given information

The given data table is

Step 2. Explanation

As the cumulative grade-point average is dependent on the number of hours spent playing video games. 

So, the number of hours spent playing video games is the independent variable and cumulative grade-point average is the dependent variable.

Part (b) Step 1. Scatter plot

The scatter plot of the given data is

Part (c) Step 1. Draw the best fit line.

Using a graphing utility the line of best fit that models the relation between number of hours of video game playing each week and grade-point average.

And the model using function notation is y = -0.094185x + 3.276344

Part (d) Step 1. Write the Slope from the obtained model.

The slope of the best fit line is -0.094185.

Part (e) Step 1.

The grade-point average of a student who plays video games for 8 hours each week is 2.31 and 2.54

Part (f) Step 1. Predict the grade-point average of a student.

A student whose grade-point average is 2.40 Plays for at least

$\begin{array}{rcl}2.40& =& -0.094185x+3.276344 \\ 2.40 - 3.276344& =& -0.094185x\\ -0.876344& =& -0.094185x\\ x& =& 9.30449\end{array}$