Q. 19 - 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(0, -5); slope =$-\frac{1}{4}$ .

Step-by-Step Solution

Answer

The sketch is:

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

Step-1 – Given

The given coordinate and slope of the point is: $P\left(0,-5\right);\text{ slope}=-\frac{1}{4}$.

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

So, 

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

Then we sketch the line$x+4y=-20$.

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

Plug x = 0

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

Plug x = 1

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

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