Chapter 11.1, Problem 32PPS

(a)

To determine

To Draw:The graph of the lines on the same plane.

Answer to Problem 32PPS

  

Explanation of Solution

Given: In this problem you will investigate parallel lines on the coordinate plane. Line $f$ passes through the point $(0,2),(2,3)$ . Line $g$ passes through the $(0,-3),(2,-2)$ and line $h$ passes through $(1,0),(2,-2)$

Graph the three lines on the same coordinate plane. Label each line.

The graph of the three lines is shown below

  

(b)

To determine

To Describe: The angles formed by the line.

Answer to Problem 32PPS

Supplementary angles

Explanation of Solution

Given: In this problem you will investigate parallel lines on the coordinate plane. Line $f$ passes through the point $(0,2),(2,3)$ . Line $g$ passes through the $(0,-3),(2,-2)$ and line $h$ passes through $(1,0),(2,-2)$

The angles formed by these lines when added are supplementary angles

(c)

To determine

To Describe: The relationship between slopes of parallel lines.

Answer to Problem 32PPS

Equal slopes

Explanation of Solution

Given: In this problem you will investigate parallel lines on the coordinate plane. Line $f$ passes through the point $(0,2),(2,3)$ . Line $g$ passes through the $(0,-3),(2,-2)$ and line $h$ passes through $(1,0),(2,-2)$

The graph is

  

We know that when the lines are parallel, the slope will be equal.

Thus

Slope of line $f$

  $=\frac{x_2-x_1}{y_2-y_1}=\frac{3-2}{2-0}=\frac{1}{2}$

Slope of line $g$

  $=\frac{x_2-x_1}{y_2-y_1}=\frac{-2-(-3)}{2-0}=\frac{1}{2}$

Since the line are parallel the slope are equal.