Q. 17 - Geometry

Question

In Exercises 16-19 a point P on a line and the slope of the line are given. Sketch the line and find the coordinates of two other points on the line.

17. P(-3, 0); slope =$\frac{2}{5}$ .

Step-by-Step Solution

Answer

The sketch is:

The equation of line is$5y-2x=6$ and the other two points on the line are

$\left(0,\frac{6}{5}\right)\text{ and }\left(1,\frac{8}{5}\right)$ 

Step-1 – Given

The given coordinate and slope of the point is:$P\left(-3,0\right);\text{ slope}=\frac{2}{5}$ .

Step-2 – To determine

We have to sketch the line and find the coordinates of two other points on the line.

Step-3 – Calculation

We’ll use the point-slope formula.

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

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

So, 

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

Then we sketch the line$5y-2x=6$ .

Now we use hit and trial method to get the other two points.

Plug x = 0

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

Plug x = 1

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

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