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Equations!
Provided with two lines, you can find the slopes of each line. If the slopes of both lines are equal, you know something special about the lines!
All About Lines
There exists no
rise in horizontal
lines.
Zero divided by anything is 0. Therefore, the slope of a horizontal line is 0.
There exists no run in vertical lines because the x value never changes.
It is impossible to divide by zero!
Therefore, there does not exist a slope.
If lines have the same slope but also have the same intercepts, then they are not parallel. They are the same line.
You can test if lines have the same intercept by manipulating the equations into the slope-intercept form. Then if the intercepts are equal, the lines are the same.
We can also identify slopes when lines are given in equation form!
Remember: If you want to
a
l
,
get a slope in the form
b
Positive Slope
Negative Slope
Lines are perpendicular if their slopes are opposites (negative reciprocals of one another).
then you can simply put a 1 on the bottom. Any number divided by 1 is equal to that number!
Rise=
Run=
Rise
Slope=
=
Run
Also, if the slopes are opposites, then there product will be -1.
the change in y, between two points, divided by the change in x, between two points.