Chapter 3.3, Problem 57HP

To determine

To generalize a method to find additional points by given information.

Answer to Problem 57HP

Generalized method to get the points on the line shall be $\left(x+1,y-2\right)$

Where x and y are the points on the line.

Explanation of Solution

Given information :

line contains the points X(3, -1) and Y(-1, 7)

Here first we shall calculate the slope of the line.

Slope of the line is given by,

  $m=\frac{y_2-y_1}{x_2-x_1}$

Now we put the values of the given points we get,

  $m=\frac{7-\left(-1\right)}{-1-3}=\frac{8}{-4}=-2$

Hence the slope is -2.

Now we know that the line will move 2 points down and 1 unit to the right from any point on the line.

Generalized method to get the points on the line shall be $\left(x+1,y-2\right)$

Where x and y are the points on the line.

Hence the points on the line shall be ((3+1), (-1-2)) = (4, -3)

Similarly after this ((4+1), (-3-2)) = (5, -5)

And this goes on.