Chapter 13.2, Problem 19WE

To determine

To sketch the line and find the coordinates of two other points on the line.

Answer to Problem 19WE

The equation of line is $x+4y=-20$ and other two points on the line are $\left(0,-5\right)\text{ and }\left(4,-6\right)$ .

Explanation of Solution

Given:

A point $P$ on a line and the slope of the line are

  $P\left(0,-5\right);\text{ slope}=-\frac{1}{4}$

Calculation:

Since the equation of line when its slope and one of point on a line is given is given by

  $y-y_1=m\left(x-x_1\right)$ , where $m$ is the slope of line .

Here, $P\left(0,-5\right);\text{ slope}=-\frac{1}{4}$

So,

  $\begin{array}{l}y-\left(-5\right)=-\frac{1}{4}\left(x-0\right)\\ 4y+20=-x\\ x+4y=-20\end{array}$

Below is the sketch of line $x+4y=-20$

  

Now, by hit and trial method

Put $x=0$

  $\begin{array}{l}x+4y=-20\\ 0+4y=-20\\ y=-5\end{array}$

Put $x=4$

  $\begin{array}{l}x+4y=-20\\ 4+4y=-20\\ y=-6\end{array}$

Therefore , the equation of line is $x+4y=-20$ and other two points on the line are $\left(0,-5\right)\text{ and }\left(4,-6\right)$ .