Q. 15 - Precalculus Enhanced with Graphing Utilities

Question

Plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

$(2,3);(4,0)$

Step-by-Step Solution

Answer

The slope of the line is $-\frac{3}{2}$ and the graph is

Step 1. Given Information

The given points are $(2,3);(4,0)$

Step 2. Calculation

Use the slope formula to find the slope of the line between the given points.

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{0-3}{4-2} \\ =\frac{-3}{2} \end{gathered}$$

Step 3. Graph

With the slope we can interpret that if x increases by 2 units then y will derease by 3 units. So, the average rate of change of y with respect to x is $-\frac{3}{2}$

The line is graphed by drawing a line passing through the points.