Q. 32 - 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 2, Point $(-2,3)$

Step-by-Step Solution

Answer

The three additional points can be $(-1,5),(-3,1),(-4,-1)$

Step 1. Given Information

The given data is slope 2, point $(-2,3)$

Step 2. Explanation

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

The slope is 2 which means that for every horizontal movement or run of 1 unit, there will be corresponding vertical movement or rise of 2 units.

Start at the given point move 1 unit horizontally to the right and 2 units vertically up to get the first point on the line that is $(-1,5)$.

We can also rewrite the slope as $\frac{-2}{-1}$.

Start from the point $(-2,3)$. Since both the numerator and denominator are negative, move 1 unit to the left and 2 units down to get another point. Thus, the point obtained is $(-3,1)$.

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

Thus, we get the third point $(-4,-1)$