Chapter 8.8, Problem 29PPS

To determine

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

Answer to Problem 29PPS

Equation of line is $2y=x-6$

Explanation of Solution

Given information: Pair of points are $\left(2,-2\right)$ and $\left(4,-1\right)$

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 $\left(2,-2\right)$ and $\left(4,-1\right)$

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,

  $y-\left(-2\right)=\frac{-1-\left(-2\right)}{4-2}\left(x-2\right)$

On solving the above equation,

  $\begin{array}{l}y+2=\frac{-1+2}{4-2}\left(x-2\right)\\ y+2=\frac{1}{2}\left(x-2\right)\\ 2\left(y+2\right)=1\left(x-2\right)\\ 2y+4=x-2\\ 2y=x-2-4\\ 2y=x-6\end{array}$

Hence, the equation of line is $2y=x-6$