Chapter 8, Problem 14MCQ

To determine

To find:

The slope of the line that passes through the given points.

Answer to Problem 14MCQ

The slope of the line passing through the given points is undefined.

Explanation of Solution

Given:

Two points on a line:

  $(-1,2)\text{and (}-\text{1,6})$ .

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:

Let point $(-1,2)=(x_1,y_1)\text{and (}-\text{1,6})=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{6-2}{-1-(-1)}\\ m=\frac{4}{-1+1}\\ m=\frac{4}{0}\end{array}$

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