Exercise 18 Page 181

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

Are They Parallel?

We will write each equation in slope-intercept form. Let's start with line a. y = 6x-2 Since it is already in the Slope-Intercept Form, we can conclude that the slope of the line a is 6. Now, let's take a look at the line b.

The slope of the line b is - 16. Last, let's take a look at the line c. y+6x=1 ⟺ y= - 6x+1 The slope of the line c is - 6. Now that we have identified the slope of each line, let's see them together at a table.

As we can see from the table, none of the lines have the same slope. Therefore, they are not parallel.

Are They Perpendicular?

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

Therefore, lines a and b are perpendicular. We will use a similar method to check if lines a and c or b and c are perpendicular.

We have found that lines a & b are perpendicular to one another.