Chapter 8.8, Problem 48STP

To determine

The correct equation from the following four options by using the table data:

Number of DVD’s	Cost   $\$$
$2$	$16$
$4$	$22$
$6$	$28$
$8$	$34$

  $3x+y=10$

  $x-3y=-10$

  $3x-y=-10$

  $x+y=10$

Answer to Problem 48STP

The correct option is C: $3x-y=-10$

Explanation of Solution

Given:

Number of DvD’s	Cost   $\$$
$2$	$16$
$4$	$22$
$6$	$28$
$8$	$34$

Concept Used:

The slope intercept form is:

  $y=mx+b$

Where,

Slope: $m$

  $y$ -intercept: $b$

Calculation:

Now, take the data points as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(2,16\right)\\ B=\left(x_2,y_2\right)=\left(4,22\right)\\ C=\left(x_3,y_3\right)=\left(6,28\right)\\ D=\left(x_4,y_4\right)=\left(8,34\right)\end{array}$

Now, the slope is calculated as:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{22-16}{4-2}\\ m=\frac{6}{2}\\ m=3\end{array}$

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

  $\begin{array}{l}y=mx+b\\ y=3x+b\end{array}$

Now, need to put $\left(2,16\right)$ in $y=3x+b$ :

  $\begin{array}{l}y=3x+b\\ 16=3\times 2+b\\ 10=b\\ b=10\end{array}$

So, the final slope-intercept form is written as:

  $\begin{array}{l}y=3x+b\\ y=3x+10\\ 3x-y=-10\end{array}$

The correct option is C: $3x-y=-10$

Conclusion:

Hence, the final slope-intercept form is $3x-y=-10$ .