Q. 16 - 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.

 P(-2, 1); slope =$\frac{1}{3}$ .

Step-by-Step Solution

Answer

The sketch is:

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

Step-1 – Given

The given coordinate and slope of the point is:$P\left(-2,1\right);\text{ slope}=\frac{1}{3}$ .

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

So, 

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

Then we sketch the line$x-3y=-5$ .

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

Plug x = 0

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

Plug x = 1

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

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