Chapter 8.4, Problem 5E

To determine

To tell:

Whether the slope of the given line is positive , negative , zero , or undefined . Then find the slope.

Answer to Problem 5E

The slope of the linepassing through the given points is $\frac{2}{3}$ and positive.

Explanation of Solution

Given:

A graph:

Concept used:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1},\text{where,}\\ m=\text{Slope of line,}\\ y_2-y_1=\text{Difference between two }y\text{-coordinates}\\ x_2-x_1=\text{Difference between two }x\text{-coordinates of same }y-\text{coordinates}\end{array}$

Calculation:

Upon looking at our given graph, we can see that as x increases the y also increases and line is going uphill, so slope of the given line is positive.

Now we will find the slope of line.

Let point $(0,-3)=(x_1,y_1)\text{and (3,}-1)=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-1-(-3)}{3-0}\\ m=\frac{-1+3}{3}\\ m=\frac{2}{3}\end{array}$

Therefore, the slope of the line passing through the given points is $\frac{2}{3}$ and positive.