Chapter 2, Problem 1RE

(a)

To determine

The slope of the line containing the points $\left(0,0\right)\text{ and }\left(4,2\right)$.

Answer to Problem 1RE

The slope of the line containing the points $\left(0,0\right)\text{ and }\left(4,2\right)$ is $\underset{\_}{\frac{1}{2}}$.

Explanation of Solution

Definition used:

“Slope:

Let $P=\left(x_1,y_1\right)\text{ and }Q=\left(x_2,y_2\right)$ be two distinct points. If $x_1\ne x_2$, the slope m of the non-vertical line L containing P and Q is defined by the formula $m=\frac{y_2-y_1}{x_2-x_1}\left(x_1\ne x_2\right)$.

If $x_1=x_2$, L is a vertical line and the slope m of L is undefined.”

Calculation:

Evaluate the slope of the line containing the points $\left(0,0\right)\text{ and }\left(4,2\right)$ as follows.

$\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{2-0}{4-0}\\ =\frac{2}{4}\\ =\frac{1}{2}\end{array}$

Therefore, the slope of the line containing the points $\left(0,0\right)\text{ and }\left(4,2\right)$ is $\underset{\_}{\frac{1}{2}}$.

(b)

To determine

To interpret: The slope of the line containing the points $\left(0,0\right)\text{ and }\left(4,2\right)$.

Explanation of Solution

From pat (a), the slope of the line is $\frac{1}{2}$.

Note that the slope can be written as $\text{Slope}=\frac{\text{Rise}}{\text{Run}}$.

This implies that, for every horizontal movement of 2 units to the right, there will be a vertical movement of 1 unit.