Question

Consider the line .y=-2/3 x+69
Find the equation of the line that is parallel to this line and passes through the point .(9,4)

Find the equation of the line that is perpendicular to this line and passes through the point .(9,4)

Answer 1

can you tell me the slope of that line (in the equation)?

Answer 2

-2/3

Answer 3

hey i wrote it wrong

Answer 4

its 6 not 69

Answer 5

oh ok. pretty similar still.
so the equation for a line (including that one) is y = mx + b

we know that m = -2/3. and we want a line that passes through (9,4), aka x=9, y=4. so we can solve for b.

Answer 6

\[y = mx+b\]\[4 = -\frac{2}{3}*9 + b \]

Answer 7

think ya can solve that?

Answer 8

it is asking for a perpendicular and parallel so two different answers

Answer 9

right. this is just for the first part. it's a two part question.

Answer 10

this is the equation of the first line, but we need to solve for b to get it. we'll get to the second one in a sec :p

Answer 11

aww ok so were finging the slope right now?

Answer 12

b=y+6

Answer 13

oh no, sorry. i guessed i skipped over that, heh.

when lines are parallel, their slopes are the same. so we have a first line with a certain slope, and we want a second line that will also have that same slope. they will be parallel (never intersecting).

when lines are perpendicular, their slopes are "reciprocals," meaning flipped sorta. the reciprocal of 2 is 1/2 (because 2 = 2/1). the reciprocal of 3/4 is 4/3.

Answer 14

\[ -\frac{2}{3}*9 = -\frac{18}{3} = -6\]

Answer 15

if they're perpendicular they have to be opposite reciprocals, so 2 would be -1/2

Answer 16

oops. good catch stacey! must be getting sleepy.

Answer 17

man this is hard stuff i dont know how you guys can do this

Answer 18

it's not too bad once it clicks. you just need to stick with it and try not get frustrated. it becomes difficult to learn at that point.

so we need a line. we know an equation for a line is:
y = m*x + b.

we need to know 'm' and 'b' though, in order to make it an actual equation.
we know m is slope. and since this line is parallel to our other line, it has the same slope.

now we just need to solve for b and we'll have an equation :)

Answer 19

lost? lol

Answer 20

yes i am =/

Answer 21

any place in particular?

Answer 22

do you follow any of what i said just above^^

Answer 23

-2/3*9 is that what i have to do to get the b?

Answer 24

sorta. don't jump too far ahead.

do you understand where I got\[4 = -\frac{2}{3}*9 + b\]from?

Answer 25

aww..ok so then if i follow through witht hat then b =10

Answer 26

yup :)

Answer 27

so substitute 'm' and 'b' into our equation for a line

Answer 28

would m be 6

Answer 29

m is our slope, which we know is the same as the other line, -2/3

Answer 30

so 4=-2/3*9+10

Answer 31

yea but you can leave y and x in there.

the equation is y = -2/3*x + 10.

this is an equation of a parallel line that passes through point (9,4). you can check and plug x=9, y=4 in that equation and it should be equal.

Answer 32

aww well made that a little hard.. so then for a perp. line would it be the recipricle of -2/3

Answer 33

i made that a little hard***

Answer 34

heh no problemo. as long as it makes sense!

Answer 35

and yeah, we would do the same thing, but this time m = 3/2, the negative reciprocal of -2/3.

Answer 36

that would give us the equation of a perpendicular line

Answer 37

so y=3/2x+10

Answer 38

it's not necessarily 10 :p.

you'll have to use 'b' and solve for b.

Answer 39

so ill have to do the same equation but change the slope

Answer 40

no you need to find the y-intercept, b. you know the slope is 3/2.

Answer 41

b=-19/2

Answer 42

i think you're right. :) let me double check. can you put the equation together now?

Answer 43

yeah that helped out a lot
ty

Answer 44

np :)

Answer 45

you're right, ps. nice job!

Answer 46

sweet got a few more problems like this i think ill be able to do now!

Answer 47

well i have another question if the slope is 7 the recipricle would be what?

Answer 48

like -1/7