Chapter 5.7, Problem 6STP

Use the scatter plot to answer the following questions.

a. What is an equation of the trend line for the data?

b. What would the earnings be for 40 hours worked?

To determine

To calculate:Use the scatter plot to answer the questions. What is an equation of the trend line for the data?

  

Answer to Problem 6STP

The equation of line is $y=9x+26$

Explanation of Solution

Given:

We can choose the values from the given data

Calculation:

Let $x$ be the number hours worked and $y$ be the earnings and we choose 2 points from the graph, i.e. $\left(x_1,y_1\right)=\left(1,35\right)\&\text{}\text{}\left(x_2,y_2\right)=\left(6,80\right)$

The equation of a line in point-slope form is $y-y_1=m\left(x-x_1\right)$

By putting above values in the point-slope form, we get

  $y-35=m\left(x-1\right)$

  $m$ is slope of the line and we can find slope using $m=\frac{y_2-y_1}{x_2-x_1}$

  $m=\frac{80-35}{6-1}=\frac{45}{5}=9$

By putting slope in the above equation, we get

  $y-35=9\left(x-1\right)$

  $y-35=9x-9$

  $y=9x+26$

Conclusion:

The equation of line is $y=9x+26$

To determine

To calculate: Use the scatter plot to answer the questions. What would be the earnings be for 40 hours worked?

  

Answer to Problem 6STP

The earnings would be $386 for 40 hours worked

Explanation of Solution

Given:

From the above part we know that the equation of trend line is $y=9x+26$

Calculation:

We have to find the value of $y$ at $x=40$

By putting $x=40$ in the above equation we get

  $\begin{array}{l}y=9*40+26\\ y=360+26\\ y=386\end{array}$

Conclusion:

The earnings would be $386 for 40 hours worked.