Exercise 6 Page 242

Two lines are parallel if their slopes are identical. To tell if two lines are perpendicular, we check if their slopes are opposite reciprocals. Let's tackle these questions one at a time.

Are They Parallel?

To start, let's write each equation in slope-intercept form, highlighting their slopes.

Now that we have identified the slope of each line, we can see that none of the lines have the same slope, so they are not parallel.

Are They Perpendicular?

To determine whether or not they are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals - 1 are opposite reciprocals, and are therefore perpendicular. Let's start with checking lines a and b.

m_1* m_2? =- 1

SubstituteII

m_1= 1/2, m_2= 1/3

1/2 * 1/3? =- 1

MultFrac

Multiply fractions

1/6≠- 1 *

Therefore, lines a and b are not perpendicular. We will use a similar method to check if lines a and c or b and c are perpendicular.

Lines	Slope 1	Slope 2	Product
a & b	1/2	1/3	1/6
a & c	1/2	-1/2	-1/4
b & c	1/3	-1/2	-1/6

We have found that none of the lines are perpendicular.

Alternative Solution

Another Approach

We can also determine whether the graphs of the given equations are parallel or perpendicular by graphing them on one coordinate plane.

From the graph, we can see that the lines are neither parallel nor perpendicular.