Chapter 8.4, Problem 10E

To determine

To tell:

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

Answer to Problem 10E

The slope of the linepassing through the given points is undefined.

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 our given line is a vertical line and as y increases the xremains same. We can see that the line has no run, so slope of the given line would be undefined.

Now we will find the slope of line.

Let point $(-1,3)=(x_1,y_1)\text{and (}-1,-2)=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-2-3}{-1-(-1)}\\ m=\frac{-5}{-1+1}\\ m=\frac{5}{0}\end{array}$

Therefore, the slope of the line passing through the given points isundefined.