Chapter 8.8, Problem 34PPS

To determine

Calculate the equation in point slope form.

$x$	$-1$	$1$	$2$	$3$
$y$	$4$	$6$	$7$	$8$

Answer to Problem 34PPS

The slope of intercept form equation is $y=1x+6$ .

Explanation of Solution

Given:

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

$x$	$-1$	$1$	$2$	$3$
$y$	$4$	$6$	$7$	$8$

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,

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(-1,4\right)\\ B=\left(x_2,y_2\right)=\left(1,6\right)\\ C=\left(x_3,y_3\right)=\left(2,7\right)\\ D=\left(x_4,y_4\right)=\left(3,8\right)\end{array}$

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

  $m=\frac{y_3-y_1}{x_3-x_1}=\frac{7-4}{2-\left(-1\right)}=\frac{3}{3}=1$

Now, the slope intercept form equation is written as:

  $\begin{array}{l}y=mx+b\\ y=1x+b\end{array}$

So, got the Y-intercept is the point $\left(0,b\right)$ . From the given points: $\left(1,6\right)$ .

So, the final slope intercept form equation is:

  $\begin{array}{l}y=mx+b\\ y=1x+6\end{array}$

Conclusion:

Hence, the slope of intercept form equation is $y=1x+6$ .