Q. 33 - 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 $-\frac{3}{2}$, Point $(2,-4)$

Step-by-Step Solution

Answer

The three additional points can be $(4,-7),(6,-10),(8,-13)$

Step 1. Given Information

The given data is slope $-\frac{3}{2}$, point $(2,-4)$

Step 2. Explanation

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

The slope is $-\frac{3}{2}$ which means that for every horizontal movement or run of 2 unit, there will be corresponding vertical movement or rise of $-3$ units.

Start at the given point $(2,-4)$ move 2 units horizontally to the right and 3 units vertically down to get the first point on the line that is $(4,-7)$.

Move 2 units to the right of $(4,-8)$ and 3 units down to get the second point $(6,-10)$ on the line.

In order to get the third point move 2 units to the right of $(6,-10)$ and 3 units up.

We get to the point $(8,-13)$ on the line.