Chapter 8.4, Problem 16E

To determine

To find:

The coordinates of two points on the line with the given equation.Then use the points to find the slope of the line.

Answer to Problem 16E

The coordinates of two points on the line would be $(3,0)\text{and (3,}-1\text{)}$ .

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

Explanation of Solution

Given:

An equation: $x=3$

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:

We can see that our given line is a vertical line. We know that x -coordinates on a vertical line remain same. So the x -coordinate for any y -value would be $3$ .

Therefore, the coordinates of two points on the line would be $(3,0)\text{and (3,}-1\text{)}$ .

Now we will find the slope of line.

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

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

Since we got a division by 0, therefore, the slope of the line passing through the given points is undefined.