# Parallel and Perpendicular lines

#### Takitia

##### New member
Find the slope of any line perpendicular to the line through points (0,5) and
(-3, -4)

#### galactus

##### Super Moderator
Staff member
First, find the slope of your line with the given points.

Remember, rise over run: $$\displaystyle \L\\\frac{y-y_{1}}{x-x_{1}}$$

The perpendicular line will have slope which is the negative reciprocal of the line you just found.

#### Mrspi

##### Senior Member
Takitia said:
Find the slope of any line perpendicular to the line through points (0,5) and
(-3, -4)

Ok....

the slope of the line through (0, 5) and (-3, -4) is

(-4 - 5) / (-3 - 0)

or,

(-9) / (-3)

or 3

The slopes of perpendicular lines are opposite reciprocals. If one line has a slope of 3 (as your line does), then any line perpendicular to this one would have a slope which is the opposite reciprocal of 3....or 3/1. The opposite reciprocal of 3/1 is -1/3.

#### arthur ohlsten

##### Full Member
two lines are perpindicular if their slopes are m2=- 1/[m1]
the equation of a line is y=mx+b, where m is the slope of the line
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A)
find the line that passes thru [0,5] and [-3,-4]

1) y=mx+b but y=5 when x=0
5=m0+b
b=5
2) y=mx+b but y=-4 when x=-3 and b=5
-4=m[-3]+5
-9=-3m
m=3

the equation of the line is y=3x+5
[ you can check this by seeing if the two points are on the line]
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B)
write the equation of any line perpindicular to the line y=3x+5

1) for a line to be perpindicular to y=3x+5 , it must have a slope of -1/3,or - 1 over the slope of the given line

y=mx+b where m=-1/3
y=[-1/3] x + b answer

hope this helps