Chapter 1.1, Problem 22E

To determine

To find: The general linear equation for the line through the two points $\left(1,1\right)$ and $\left(2,1\right)$ .

Answer to Problem 22E

The general linear equation for the line through the two points $\left(1,1\right)$ and $\left(2,1\right)$ is $y=1$ .

Explanation of Solution

Given information: The line passes through the two points $\left(1,1\right)$ and $\left(2,1\right)$ .

Formula used: The general linear equation of a line in terms of x and y is:

  $Ax+By=C$

Calculation:

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 1 for $x_1$ , 1 for $y_1$ , 2 for $x_2$ and 1 for $y_2$ respectively in the formula of slope.

  $\begin{array}{c}m=\frac{1-1}{2-1}\\ =\frac{0}{1}\\ =0\end{array}$

The slope-intercept form of an equation of line with slope m and point $\left(x_1,y_1\right)$ is given by,

  $y=m\left(x-x_1\right)+y_1$

Substitute 1 for $x_1$ , 1 for $y_1$ and 0 for m in the above formula.

  $\begin{array}{c}y=0\left(x-1\right)+1\\ y=0+1\\ y=1\end{array}$

Therefore, the general linear equation for the line through the two points $\left(1,1\right)$ and $\left(2,1\right)$ is $y=1$ .