Q. 36 - Precalculus Enhanced with Graphing Utilities

Question

The slope and a point on a line are given. Use this information to locate three additional points on the line. Answers may vary.

Slope $-1$, Point $(4,1)$

Step-by-Step Solution

Answer

The three additional points can be $(5,0),(3,2),(2,3)$

Step 1. Given Information

The given data is slope $-1$, point $(4,1)$

Step 2. Explanation

The slope of a non vertical line is $m=\frac{rise}{run}$

The slope is $\frac{-1}{1}$ which implies that for every horizontal movement of 1 unit there will be a corresponding vertical down movement of 1 units.

Now, consider the given point, move 1 unit in the x- direction to the right and 1 unit down in the y-direction.

Thus, we get the first point as $(5,0)$

We can also rewrite the slope as $\frac{1}{-1}$.

Start from the point $(4,1)$ and move 1 uit to the left and 1 unit up to get the another point.

Thus, the point obtained as $(3,2)$.

In order to find the third point, move 1 unit to the left and 1 unit up from the point $(3,2)$

Thus, we get the third point as $(2,3)$