Chapter 1.4, Problem 24E

To determine

To find: standard form of equation for line, m.

Answer to Problem 24E

  $x+y+2=0$

Explanation of Solution

Given information:

The points on line are as follows:

  $\begin{array}{l}C\left(x_1,y_1\right)=\left(-2,0\right)\\ D\left(x_2,y_2\right)=\left(1,-3\right)\end{array}$

Calculation

The point slope form is as follows:

  $y-y_1=m\left(x-x_1\right)$ … (1)

The equation slope is as follows:

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

Substitute the value of m in equation (1) to get,

  $y-y_1=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}\left(x-x_1\right)$ … (2)

Substitute the given points in equation (2) and simply it as follows:

  $\begin{array}{l}C\left(x_1,y_1\right)=\left(-2,0\right)\\ D\left(x_2,y_2\right)=\left(1,-3\right)\end{array}$

  $\begin{array}{c}y-0=\frac{\left(-3-0\right)}{\left(2-\left(-2\right)\right)}\left(x-\left(-2\right)\right)\\ y=\left(\frac{-3}{2+4}\right)\left(x+2\right)\\ y=\left(\frac{-3}{6}\right)\left(x+2\right)\\ y=\left(\frac{-1}{2}\right)\left(x+2\right)\\ y=\left(\frac{-x}{2}\right)-1\\ 2y=-x-1\\ x+2y+1=0\end{array}$

Therefore, the standard equation of the line is $x+y+2=0$ .