Question #4c0bb
2 Answers
When given two lines in slope-intercept form:
Only the slopes play a role in determining whether the lines are parallel or perpendicular.
Explanation:
Two lines are parallel, if and only if their slopes are equal:
When the two slopes are equal, it can be said that the two lines belong to a family of lines that are parallel.
For example, we know that the two lines:
There is are two special cases for parallel lines.
1 Vertical lines are parallel; their slope is undefined and they have no y intercept. They have the form:
Any two lines of this form parallel.
2 Horizontal lines are parallel; their slope is 0. They will have different y-intercepts. They have the form:
Any two lines of this form are parallel.
NOTE: In both cases
Two lines are perpendicular, if and only if the product of their slopes is equal to -1:
When the product of the two slopes is equal to -1, it can be said that the two lines belong to a family of lines that are perpendicular.
For example, we know that the two lines:
There is a special case for perpendicular lines where one is a horizontal line and the other is a vertical line:
Any two lines of these forms are perpendicular.
NOTE:
Yes for parallel lines. Lines that are parallel cannot have the same y-intercept. If they do, then they are the same line. Two lines are perpendicular if the product of their slopes equal
Explanation:
The y-intercept is the value of
where:
Substitute
So, if the y-intercept
Parallel Lines
Example: Are the following lines parallel?
Solve for
They are the same line, so they are not parallel.
Perpendicular Lines
Example: Are the following lines perpendicular?
Multiply the slopes.
Therefore the lines are perpendicular.
Notice on the graph that the point of intersection is the y-intercept:
graph{(y-5x-8)(y+1/5x-8)=0 [-17.35, 14.67, -2.88, 13.14]}