Chapter 8.4, Problem 52E

To determine

What is the slope of the line that passes through the points $(-1,-14)\text{ and (5,4)}$ .

Answer to Problem 52E

The slope of the line passing through the given points is $3$ and option D is the correct choice.

Explanation of Solution

Given:

Four choices: $\text{A}\text{. }-3\text{ B}\text{. }-\frac{1}{3}\text{ C}\text{. }\frac{1}{3}\text{ D}\text{. 3}$

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:

Let point $(-1,-14)=(x_1,y_1)\text{and (5,4)}=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{4-(-14)}{5-(-1)}\\ m=\frac{4+14}{5+1}\\ m=\frac{18}{6}\\ m=3\end{array}$

Therefore, the slope of the line passing through the given points is $3$ and option D is the correct choice.