Chapter Test
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Parallel lines have the same slope. The slopes of perpendicular lines are negative reciprocals.
Parallel Lines: None of the lines are parallel.
Perpendicuar Lines: Lines 1 and 2 are perpendicular.
Two lines are parallel if their slopes are identical. To tell if two lines are perpendicular, we have to check if their slopes are negative reciprocals. Let's tackle these questions one at a time.
For this exercise, we have been given equations that are not in slope-intercept form, so let's first rewrite all of them to identify their slopes.
| Line | Given Equation | Slope-intercept form | Slope |
|---|---|---|---|
| 1 | y-c=ax | y=ax+c | a |
| 2 | ay=- x-b | y=-1/ax-b/a | -1/a |
| 3 | ax+y=d | y=- ax+d | - a |
Now that we have identified the slope of each line, we can see that none of the lines have the same slope. Therefore, none of the lines are parallel.
m_1= a, m_2= -1/a
Multiply
a/a=1
| Lines | Slope 1 | Slope 2 | Product |
|---|---|---|---|
| 1 & 2 | a | -1/a | -1 |
| 1 & 3 | a | - a | - a^2 |
| 2 & 3 | -1/a | - a | 1 |
We have found that only lines 1 and 2 are perpendicular to one another.