Chapter 9, Problem 68SGR

To determine

To find: given table represents a linear or non linear equation.

$x$	$6$	$7$	$8$	$9$
$y$	$10$	$20$	$30$	$40$

Answer to Problem 68SGR

Given table illustrate a linear equation.

Explanation of Solution

Given:

$x$	$6$	$7$	$8$	$9$
$y$	$10$	$20$	$30$	$40$

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where,

Slope: $m$

Y-intercept: $\left(0,b\right)$

Calculation:

There are seven points are given as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(6,10\right)\\ B=\left(x_2,y_2\right)=\left(7,20\right)\\ C=\left(x_3,y_3\right)=\left(8,30\right)\\ D=\left(x_4,y_4\right)=\left(9,40\right)\end{array}$

Now use any two points to calculate the slope intercept from equation:

  $m=\frac{y_3-y_1}{x_3-x_1}=\frac{30-10}{8-6}=\frac{20}{2}=10$

Now, the slope intercept form equation is written as:

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

Now put the value of $\left(x_1,y_1\right)=\left(6,10\right)$ in the above eq. to get the Y-intercept:

$\begin{array}{l}y=mx+b\\ 10=10\left(6\right)+b\\ b=60-10\\ b=50\end{array}$

So, the final slope intercept form equation is:

  $\begin{array}{l}y=mx+b\\ y=2x+50\end{array}$

By using the above data points and line of fit eq. or slope-intercept form eq. graph is plotted.

Conclusion:

Hence, Given table illustrate a linear equation.