Q. 35 - 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 $(-1,-5),(0,-7),(1,-9)$

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 $\frac{-2}{1}$ which implies that for every horizontal movement of 1 unit there will be a corresponding vertical down movement of 2 units.

Now, consider the given point, move 1 unit in the x- direction to the right and 2 units down in the y-direction.

Thus, we get the first point as $(-1,-5)$

Next, move this obtained point, 1 unit in the x- direction to the right and 2 units down in the y-direction which gives the second point on the line as $(0,-7)$

Further, move this obtained point, 1 unit in the x- direction to the right and 2 units down in the y-direction which gives the third point on the line as $(1,-9)$