Question

Marshall surveyed 12 students at estimate their exercise and television viewing habits. He created the scattered plot shown. Marshall models the data with the equation y= -1.5x +121, where x represents the number of minutes spent watching television and y represents the number of minutes spent exercising. Choose true or false for each statement based upon the model. The picture of the graph is attached here. Hope you can see it! Statement 5: if a student exercises for more than 80 minutes, the student will not watch tv? Is this one true or false?

Answer 1

y is the number of minutes spent exercising

x is the number of minutes spent wathcing TV

Linear relationship:

`y=-1.5x+121`

In the equation above:

* The -1.5 represents the rate of change; it represents the change of y for each x.

* The 121 represents the initial value of y, or the value of y when x is 0

Then, for the given statements the next two are true:

- For each additional minute spent whatching TV, the number of minutes spent exercising decreases by 1.5

- If a student watches no TV (x=0) the student will exercise for 121 minutes

Solve y in terms of x to determine if the other two statements are true:

`\begin{gathered} y-121=-1.5x \\ \\ -(1)/(1.5)y-(121)/(-1.5)=x \\ \\ \\ x=-(1)/(1.5)y+(121)/(1.5) \end{gathered}`

Then, for each additional minute spent exercising, the number of minutes spent watching TV decreases by 1/1.5 (approximately 0.66)

if a student exercises for more than 80 minutes:

`\begin{gathered} x=-(1)/(1.5)(80)+(121)/(1.5) \\ \\ x=-(80)/(1.5)+(121)/(1.5) \\ \\ x=(41)/(1.5) \\ \\ x=27.3 \end{gathered}`

Then, if the student exercises for more than 80 minutes, the time watching TV will decrease but it will not be 0 until the time exercising is

Answer:

1. True

2. False

3. False

4. True