Chapter 8.8, Problem 35PPS

To determine

Calculate the equation in point slope form.

$x$	$-2$	$-1$	$1$	$2$
$y$	$-4$	$-2$	$2$	$4$

Answer to Problem 35PPS

The slope of intercept form equation is $y=2x$ .

Explanation of Solution

Given:

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

$x$	$-2$	$-1$	$1$	$2$
$y$	$-4$	$-2$	$2$	$4$

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,

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(-2,-4\right)\\ B=\left(x_2,y_2\right)=\left(-1,-2\right)\\ C=\left(x_3,y_3\right)=\left(1,2\right)\\ D=\left(x_4,y_4\right)=\left(2,4\right)\end{array}$

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

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-\left(-4\right)}{-1-\left(-2\right)}=\frac{2}{1}=2$

Now, the slope intercept form equation is written as:

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

So, got the Y-intercept is the point $\left(0,b\right)$ . From the given points: $\left(-1,-2\right)$ .

So, the final slope intercept form equation is:

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

Conclusion:

Hence, the slope of intercept form equation is $y=2x$ .