Q. 18 - 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, 4); slope =$-\frac{3}{2}$ .

Step-by-Step Solution

Answer

The sketch is:

The equation of line is$2y+3x=14$ and the other two points on the line are$\left(0,7\right)\text{ and }\left(1,\frac{11}{2}\right)$.

Step-1 – Given

The given coordinate and slope of the point is:$P\left(2,4\right);\text{ slope}=-\frac{3}{2}$ .

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,$P\left(2,4\right);\text{ slope}=-\frac{3}{2}$ .

So, 

$\begin{array}{l}y-4=-\frac{3}{2}\left(x-2\right)\\ 2y-8=-3x+6\\ 2y+3x=14\end{array}$

Then we sketch the line .

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

Plug x = 0

$\begin{array}{l}2y+3x=14\\ 2y+3\left(0\right)=14\\ y=7\end{array}$

Plug x = 1

$\begin{array}{l}2y+3x=14\\ 2y+3\left(1\right)=14\\ y=\frac{11}{2}\end{array}$

So, the equation of line is$2y+3x=14$ and the other two points on the line are 

$\left(0,7\right)\text{ and }\left(1,\frac{11}{2}\right)$