Question

I really need help at understanding perpendicular lines. I kinda understand paralel lines, but not so well. My teacher quickly brushed over it and we have a test tommorow but I don't know anything about it :( I need to find perpendicular lines without a graph and she didnt teach us it.

Answer 1

so you're given equations?

Answer 2

Yeah. She said inn the test she will give us in y=mx+b and (x,y).

Answer 3

do you have a sample problem?

Answer 4

no

Answer 5

do you want me to make one up?

Answer 6

If you can that would be great :P

Answer 7

What is the equation of the perpendicular line to y = 3x+7 and this perpendicular line goes through (1,5)

Answer 8

Im not quite sure how to find it :(

Answer 9

what is the slope of y = 3x+7

Answer 10

3

Answer 11

you can think of 3 as the fraction 3/1

since 3/1 = 3

Answer 12

ok

Answer 13

take the original slope and flip the fraction

3/1 --> 1/3

then flip the sign

+1/3 --> -1/3

Answer 14

original slope: 3/1

perpendicular slope: -1/3

Answer 15

oh

Answer 16

that is it?

Answer 17

we know two things

perpendicular slope: m = -1/3

the perpendicular line goes through the point (x,y) = (1,5)

Answer 18

so you take m = -1/3, x = 1, y = 5 and plug them into y = mx+b

Answer 19

and then solve for b

Answer 20

so it would be 5=1/3(1/1)+b before simpylfying?

Answer 21

if you mean

\[\Large 5 = \frac{1}{3}\left(\frac{1}{1}\right) + b\]

then yes. Now you solve for b

Answer 22

oops

Answer 23

the 1/3 should be negative

Answer 24

\[\Large 5 = -\frac{1}{3}\left(\frac{1}{1}\right) + b\]

Answer 25

ok so it would be like 5= -1/3+b then divide 5 by -1/3 which would be -15

Answer 26

so b=-15?

Answer 27

you add 1/3 to both sides to move that 1/3 over, which isolates b

Answer 28

oh so it'll actually be\[5 \frac{ 1 }{ 3 }=b\]

Answer 29

correct since \[\Large 5 + \frac{1}{3} = 5 \frac{1}{3}\]

Answer 30

oh cool!

Answer 31

so then what do we do after that?

Answer 32

m = -1/3 and b = 5 & 1/3

so you have enough info to know the full perpendicular equation in y = mx+b form

Answer 33

so y= -1/3+5 and 1/3 is the perpendicular line?

Answer 34

more like

\[\Large y = -\frac{1}{3}x + 5 \frac{1}{3}\]

Answer 35

right i forgot the x

Answer 36

since 5 & 1/3 = 16/3, we can also write it as

\[\Large y = -\frac{1}{3}x + \frac{16}{3}\]

Answer 37

you are a life saver :D

Answer 38

thank you so much!

Answer 39

you're welcome

here is more practice

http://www.mathworksheets4kids.com/straight-lines/perpendicular-lines-equations.pdf

it offers practice problems & answers as well (just not steps)

Answer 40

thank you :)))

Answer 41

i wish my teacher explained like you xD lol

Answer 42

no problem