Chapter 1.1, Problem 23E

To determine

To find: The general linear equation for the line through the two points $\left(-2,0\right)$ and $\left(-2,-2\right)$ .

Answer to Problem 23E

The general linear equation for the line through the two points $\left(-2,0\right)$ and $\left(-2,-2\right)$ is $x=-2$ .

Explanation of Solution

Given information: The line passes through the two points $\left(-2,0\right)$ and $\left(-2,-2\right)$ .

Calculation:

The general linear equation of a line is $Ax+By=C$ .

The formula for the slope of a line that passes through points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute $-2$ for $x_1$ , 0 for $y_1$ , $-2$ for $x_2$ and $-2$ for $y_2$ respectively in the formula of slope.

  $\begin{array}{c}m=\frac{-2-0}{-2-\left(-2\right)}\\ =\frac{-2}{0}\end{array}$

The slope of the line passing through the given points is not defined. So, the linear equation is a vertical line.

  $x=-2$

Therefore, the general linear equation for the line through the two points $\left(-2,0\right)$ and $\left(-2,-2\right)$ is $x=-2$ .