Chapter 0.1, Problem 6E

a.

To determine

To Plot: The given points $A$ and $B$

Explanation of Solution

Given:

  $A\left(-2,-1\right),B\left(1,-2\right)$

Graph:

To plot a point based on the ordered pair $\left(a,b\right),$ follow these steps:

First, depending on whether the sign of the unit is positive or negative, move the unit $\left|a\right|$ to the right or left from the origin.

After that, move $\left|b\right|$ units up/down accordingly depending on its sign.

Plot $A\left(-2,-1\right),B\left(1,-2\right)$

  

b.

To determine

The slope of the line $L$

Answer to Problem 6E

The slope of the line $L$ is $m=\frac{-1}{3}$

Explanation of Solution

Given:

  $A\left(-2,-1\right),B\left(1,-2\right)$

Slope of the line joining two points $P_1=\left(x_1,y_1\right)$ and $P_2=\left(x_2,y_2\right)$ is

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute $x_1=-2,y_1=-1$ and $x_2=1,y_2=-2$ in the slope formula:

  $m=\frac{-2-\left(-1\right)}{1-\left(-2\right)}$

Simplify both the numerator/denominator

  $\begin{array}{l}m=\frac{-2+1}{1+2}\\ m=\frac{-1}{3}\end{array}$

Thus, the slope is $m=\frac{-1}{3}$ .

c.

To determine

To Draw: The graph of line $L$

Explanation of Solution

Given:

  $A\left(-2,-1\right),B\left(1,-2\right)$

Sketch the line for the given points $A\left(-2,-1\right),B\left(1,-2\right)$