Chapter 8.10, Problem 35SR

To determine

The equation in the slope intercepts form for the following table:

$x$	$y$
$-1$	$-7$
$0$	$-3$
$1$	$1$
$2$	$5$

Answer to Problem 35SR

The required equation is $y=4x-3$ .

Explanation of Solution

Given:

The values of $x$ and $y$ are expressed in the table form as:

$x$	$y$
$-1$	$-7$
$0$	$-3$
$1$	$1$
$2$	$5$

Concept Used:

The slope intercept form equation is

  $y=mx+b$

Where;

Slope: $m$

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

Calculation:

There are four points are given as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(-1,-7\right)\\ B=\left(x_2,y_2\right)=\left(0,-3\right)\\ C=\left(x_3,y_3\right)=\left(1,1\right)\\ D=\left(x_4,y_4\right)=\left(2,5\right)\end{array}$

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

  $m=\frac{y_3-y_1}{x_3-x_1}=\frac{1-\left(-7\right)}{1-\left(-1\right)}=8/2=4$

Now, the slope intercept form equation is written as:

  $\begin{array}{l}y=mx+b\\ y=4x+b\end{array}$

So, got the Y-intercept is the point $\left(0,b\right)$ . From the given points: $\left(0,-3\right)$ .

So, the final slope intercept form equation is:

  $\begin{array}{l}y=mx+b\\ y=4x-3\end{array}$

Conclusion:

Hence, the slope intercept form equation is $y=4x-3$ .