Chapter 8.8, Problem 32PPS

To determine

The equation for the line that passes through each pair of points.

Answer to Problem 32PPS

The equation for the line passes through each pair of points are

  $\begin{array}{l}y=-\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$6$}\right.+-10\\ y=-\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$6$}\right.-10\end{array}$

Explanation of Solution

Given: The points of each line $\left(4,-4\right)$ and $\left(8,-10\right)$

Concept Used:

The Slope can be found by the following formula:

  $m=\frac{y_2-y_1}{x_2-x_1}$

In this, $m$ is the slope and $\left(x_1,y_1\right)$

  $\left(x_2,y_2\right)$ are the given points on the line.

Calculation:

Given that the passing points are $\left(4,-4\right)$ and $\left(8,-10\right)$

Substituting the values from the points in the problem gives:

  $m=\frac{-10-4}{8-(-4)}=\frac{-10-4}{8+4}=\frac{-14}{12}=-\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$

The point $\left(8,-10\right)$ is the $y-$ intercept.

With the help of slope formula write the equation of the line. The slope intercept form of a linear equation is:

  $y=mx+b$

Where $m$ the slope of is $b$ the $y-$ intercept value.

Substituting the slope the calculated and the $y-$ intercept from the problem provides:

  $\begin{array}{l}y=-\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$6$}\right.+-10\\ y=-\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$6$}\right.-10\end{array}$

Conclusion:

Hence, the equation for the line passes through each pair of points are

  $\begin{array}{l}y=-\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$6$}\right.+-10\\ y=-\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$6$}\right.-10\end{array}$ .