Question

write an equation of the line that passes through (2,-7) and is parallel to the line x=5. Please show all steps!

Answer 1

x=2 line

Answer 2

Please show your work

Answer 3

there is nothing in this very easy ...which is the line parallel to x=5 and passing through the point x=2 ...the only possibility is x=2 line

Answer 4

hmmm

Answer 5

understood?

Answer 6

kind of, i still need to show some sort of work of how i get the answer though

Answer 7

ok wait a sec?

Answer 8

ok :)

Answer 9

It would help if you used equations like y=mx+b in order to show me :)

Answer 10

a line with equation x=5 has slope equal to \(\infty\) (becuase it is a vertical line)
ok?

Answer 11

look at the graph once vertical axis is x axis

Answer 12

@helder_edwin ok...and?

Answer 13

well this is not exactly correct but u can think of the slope as
\[\large m=\frac{k}{0} \]
where k is any constant.

Answer 14

now the formula for the slope is
\[\large m=\frac{y_1-y_2}{x_1-x_2} \]
replacing m above and the point given u would get
\[\large \frac{1}{0}=\frac{y-(-7)}{x-2}=\frac{y+7}{x-2} \]
and from this
\[\large 1(x-2)=0(y+7)\]
or
\[\large x-2=0 \qquad\text{or}\qquad x=2 \]

Answer 15

in that sense literally by applying the line equation of a line with slope m and passes through a point (x*,y*) is
y-y* = m(x-x*)
following this
(y-(-7)) =infinity ( x-2)
(y+7)/infinity = x-2
but any number/infinity = 0
therefore x-2 =0
which implies x=2 is the line.

Answer 16

got it @ineedhelp77 ??

Answer 17

I'm still thinking...

Answer 18

whats the problem?

Answer 19

It's just that the way you guys solved the problem is waaaaaaaaaay different than the way I'm learning how to and my head is just spinning.

Answer 20

take your time.

Answer 21

if i were to solve this on paper, instead of writing infinity, would I write 0?

Answer 22

lets solve it your way...what is the first step which you think?

Answer 23

well, my teachers always told me to write y=mx+b first

Answer 24

actually the equation of a line in most general form is not that .that is the problem

Answer 25

No, but then I would usually take the same slope and then plug everything in

Answer 26

y = mx + c is a simplified form of a line with some conditions

Answer 27

i'll teach you the most general method if you wish which helps you solve any equation of a line

Answer 28

That would be nice! I've never even seen y=mx+c before

Answer 29

that is the same equation you wrote we always use c instead of b

Answer 30

ok lets start

Answer 31

Oh ok

Answer 32

here, we always use b

Answer 33

see first thing is to find slope ...do you know how to do this..if yes we'll go to next step

Answer 34

yes i do know

Answer 35

to remind you if m is the slope and we have two points (x1,y1) and (x2,y2)
then m=(y2-y1)/(x2-x1) ...are you ok with this?

Answer 36

yes

Answer 37

then you can write (y2-y1) = m (x2-x1) ..ok?

Answer 38

so is this how i start the problem? by writing this?

Answer 39

wait a sec let me complete...you understood the previous step?

Answer 40

yes

Answer 41

then for any general point (x,y) we can write the equation of a line by replacing (x2,y2) with (x,y)....then the equation becomes {(y-y1) = m (x-x1)} this is the equation of a line in most general form

Answer 42

ok. so how do i use it for this problem?

Answer 43

dont i need to find the slope first? how would i do that with only one point given?

Answer 44

now first find slope m=(y2-y1)/(x2-x1) but as you know x=5 line value of x is constant then slope becomes infinity...understood?

Answer 45

what should i write instead of infinity?

Answer 46

you write infinity symbol ∞

Answer 47

ok with it?

Answer 48

oh ok thanks

Answer 49

how would the distributing part work? its infinity(x-2)

Answer 50

in given question the line which we need is parallel to x=5 then its slope should also be infinity ok?

Answer 51

ok...

Answer 52

now as you can see we have slope m and a point (2,-7)

Answer 53

yes...

Answer 54

by using the equation (y-(-7)) = infinity (x-2)

Answer 55

okay i got that, but how would i distribute that

Answer 56

you know (any number/infinity )= 0 ??

Answer 57

is this understood?

Answer 58

yeah, but arnt i supposed to multiply?

Answer 59

you can take the infinity to the L.H.S and write (y+7)/infinity = (x-2)

Answer 60

ok with this?

Answer 61

LHS?

Answer 62

left hand side :)

Answer 63

oooh okayyy

Answer 64

then what do you get??

Answer 65

x=2!!! OMG THANKS SO MUCH

Answer 66

You're the best thanks so much! :D

Answer 67

if you wish i'll say something which you may follow

Answer 68

sorry, i have to go now. its dinner time and i have to finish the rest of my homework. thanks anyway though!

Answer 69

goodbye! and thanks again!

Answer 70

ok but what i wanted to say was..don't blindly follow the procedure..use ur common sense by drawing graphs...just by thinking you could solve the above problem