Chapter 13.2, Problem 16WE

To determine

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

Answer to Problem 16WE

The equation of line is $x-3y=-5$ and other two points on the line are $\left(0,\frac{5}{3}\right)\text{ and }\left(1,2\right)$

Explanation of Solution

Given:

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

  $P\left(-2,1\right);\text{ slope}=\frac{1}{3}$

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, $P\left(-2,1\right);\text{ slope}=\frac{1}{3}$

So,

  $\begin{array}{l}y-1=\frac{1}{3}\left(x-\left(-2\right)\right)\\ 3y-3=x+2\\ x-3y=-5\end{array}$

Below is the sketch of line $x-3y=-5$

  

Now, by hit and trial method

Put $x=0$

  $\begin{array}{l}x-3y=-5\\ 0-3y=-5\\ y=\frac{5}{3}\end{array}$

Put $x=1$

  $\begin{array}{l}x-3y=-5\\ 1-3y=-5\\ y=2\end{array}$

Therefore , the equation of line is $x-3y=-5$ and other two points on the line are $\left(0,\frac{5}{3}\right)\text{ and }\left(1,2\right)$ .