Chapter 13.2, Problem 17WE

To determine

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

Answer to Problem 17WE

The equation of line is $5y-2x=6$ and other two points on the line are $\left(0,\frac{6}{5}\right)\text{ and }\left(1,\frac{8}{5}\right)$ .

Explanation of Solution

Given:

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

  $P\left(-3,0\right);\text{ slope}=\frac{2}{5}$

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, $P\left(-3,0\right);\text{ slope}=\frac{2}{5}$

So,

  $\begin{array}{l}y-0=\frac{2}{5}\left(x-\left(-3\right)\right)\\ 5y=2x+6\\ 5y-2x=6\end{array}$

Below is the sketch of line $5y-2x=6$

  

Now, by hit and trial method

Put $x=0$

  $\begin{array}{l}5y-2x=6\\ 5y-2\left(0\right)=6\\ y=\frac{6}{5}\end{array}$

Put $x=1$

  $\begin{array}{l}5y-2x=6\\ 5y-2\left(1\right)=6\\ y=\frac{8}{5}\end{array}$

Therefore , the equation of line is $5y-2x=6$ and other two points on the line are $\left(0,\frac{6}{5}\right)\text{ and }\left(1,\frac{8}{5}\right)$ .