QuestionDetermine if the following lines are parallel, perpendicular, or neither: Line 1: Line 2: Line 3:
Studdy Solution
STEP 1
Assumptions1. The equations of the lines are given in the standard form .
. Two lines are parallel if their slopes are equal.
3. Two lines are perpendicular if the product of their slopes is -1.
4. The slope of a line given in the standard form is .
STEP 2
First, we need to find the slopes of the given lines. The slope of a line given in the form is .
For Line1, and , so the slope is .
STEP 3
Calculate the slope of Line1.
STEP 4
For Line2, the equation is already in the slope-intercept form , where is the slope. So, the slope of Line2 is .
STEP 5
For Line3, we can rearrange the equation to the form to find the slope.
So, the slope of Line3 is .
STEP 6
Now that we have the slopes of all three lines, we can compare them to determine if the lines are parallel, perpendicular, or neither.
First, compare the slopes of Line1 and Line2.
If , the lines are parallel.
If , the lines are perpendicular.
STEP 7
Plug in the values for and and check the conditions.
STEP 8
The first equation is not true, so Line1 and Line2 are not parallel. The second equation is also not true, so Line1 and Line2 are not perpendicular. Therefore, Line1 and Line2 are neither parallel nor perpendicular.
STEP 9
Next, compare the slopes of Line and Line3.
If , the lines are parallel.
If , the lines are perpendicular.
STEP 10
Plug in the values for and and check the conditions.
STEP 11
The first equation is not true, so Line and Line3 are not parallel. The second equation is also not true, so Line and Line3 are not perpendicular. Therefore, Line and Line3 are neither parallel nor perpendicular.
STEP 12
Finally, compare the slopes of Line2 and Line.
If , the lines are parallel.
If , the lines are perpendicular.
STEP 13
Plug in the values for and and check the conditions.
STEP 14
The first equation is true, so Line2 and Line3 are parallel. The second equation is not true, so Line2 and Line3 are not perpendicular.
In conclusion, Line is neither parallel nor perpendicular to Line2 or Line3, and Line2 is parallel to Line3.
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