Chapter 8.9, Problem 15STP

To determine

The equation of line of fit to satisfy the data points $\left(4,534\right),\left(10,138\right)$ from the following four eq. options:

A. $y=-66x+798$

B. $y=-66x-798$

C. $y=66x+798$

D. $y=66x-798$

Answer to Problem 15STP

Correct option is A. The eqn. is $y=-66x+798$

Explanation of Solution

Given:

The data points are $\left(4,534\right),\left(10,138\right)$

Concept Used:

The slope intercept form is:

  $y=mx+b$

Where,

Slope: $m$

  $y$ -intercept: $b$

Calculation:

Now, take the data points as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(4,534\right)\\ B=\left(x_2,y_2\right)=\left(10,138\right)\end{array}$

Now, the slope is calculated as:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{138-534}{10-4}\\ m=-66\end{array}$

So, the slope intercept eq. can be written as:

  $\begin{array}{l}y=mx+b\\ y=-66x+b\end{array}$

Now, need to put $\left(4,534\right)$ in $y=-66x+b$ :

  $\begin{array}{l}534=-66\left(4\right)+b\\ b=534+264\\ b=798\end{array}$

So, the final slope-intercept form is $y=-66x+798$ .

So, the option A. is correct.

Conclusion:

Hence, the final slope-intercept form is $y=-66x+798$ .