Chapter 8.8, Problem 31PPS

To determine

To calculate: To write the equation of line that passes through each pair of points

Answer to Problem 31PPS

Equation of line is $y=-6$

Explanation of Solution

Given information: Pair of points are $\left(3,-6\right)$ and $\left(5,-6\right)$

Formula Used:

Equation of line passing through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Points are $\left(3,-6\right)$ and $\left(5,-6\right)$

Equation of line passing through two points is given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Substituting the values in above equation,

  $y-\left(-6\right)=\frac{-6-\left(-6\right)}{5-3}\left(x-3\right)$

On solving the above equation,

  $\begin{array}{l}y+6=\frac{0}{2}\left(x-3\right)\\ y+6=0\left(x-3\right)\\ y+6=0\\ y=-6\end{array}$

Hence, the equation of line is $y=-6$