Question

Give an equation of the line through the point (6, 5) and parallel to the line 2x + 3y = 7.

Answer 1

You should know one thing that Parallel Lines have same Slope..

Answer 2

Here, the question says, that find the equation of a line (say l) which passes through a point (x,y) and parallel to another line (say m) with equation 2x + 3y = 7..

So, as Slopes of both the parallel lines will be same, so first step is to find the slope of the line m having equation : 2x + 3y = 7

Answer 3

Can you find the slope of equation : 2x + 3y = 7 ??

Answer 4

-2/3?

Answer 5

Oh, you are real fast..

Answer 6

This is slope of line m, so, line l should have same slope as both the lines are parallel..

Answer 7

So, line l has slope of -2/3 and you know you are given that it is passing through a point..

So, use point slope form and find the equation now..

Can you do that??

Answer 8

y-5=-2/3(x-6)

Answer 9

Point Slope Form is given as:

\(y - y_1 = m(x - x_1)\)

Answer 10

Yeah just simplify it, so that it looks nice while seeing it.. :)

Answer 11

Good, you are going real good.. :) Multiply by 3 and bring the x term on Left Hand Side...

Answer 12

OK i came up with
y=-2/3x-1
is that riht?

Answer 13

*right

Answer 14

Check it once again..

Answer 15

y-5=-2/3x+4

Answer 16

Better is to write it in the form in which the other line m is given to you: ie :

\(a_x + by = c\)

Answer 17

*\(ax\)

Answer 18

Multiply by 3 both the sides first and tell me what did you get??

Answer 19

ok so i came up with
y=-2/3x+9

oh wait where did you get the 3?

Answer 20

Look here:

You got :

\[y - 5 = -\frac{2}{3}(x -6)\]

Here multiply by 3 both the sides and now tell me what have you got?

Answer 21

that gives me
y-15=-2x-12
?

Answer 22

-12 or +12??

Answer 23

Be careful with signs..

Answer 24

ohhh ummmm +12 sorry

Answer 25

y-12=-2x+12

Answer 26

which in turn gives me
y=-2x+24?

Answer 27

Are you alright?? Have you studied more than your capacity??

Answer 28

Oh Yes I'm fine XD
I'm sorry what did I do wrong?

Answer 29

I have some trouble with these types of problems

Answer 30

On LHS, how you got y - 12??

Answer 31

You have applied method just superbly, just you are doing mistakes in calculation. Go slow and be careful..

Answer 32

*headdesk*
I have no idea how I got that...
Let me redo that starting with
y-5=-2/3(x-6)

Answer 33

Yes, now multiply 3 both the sides first.. Just do what I am saying to you..

Answer 34

Ok sorry i'm confused what do i multiply by 3?

Answer 35

Wait, I should have explain it earlier to you..

Your line m is in which form??

Answer 36

m=-2/3

Answer 37

2x + 3y = 7, the form : \(ax + by = c\) this is called Standard Form..

Answer 38

No doubt, you have got y-5 = -2/3(x-6) but it does not seem like ax + by = c to me..

Does it look like to you???

Answer 39

oHHH OK so i need to switch
y-5=-2/3(x-6)
to standard form?

Answer 40

Yes, this is what I was trying to say.. :)

Answer 41

Oh Ok sorry!
that gives me
2x+3y=0

Answer 42

Do whatever way you know, I want to bring just x and y on LHS and constants on RHS..

Now do in your way..

Answer 43

NO..

Answer 44

Oh sorry...
Ok you said times it by 3
what do i times by 3?

Answer 45

There is a reason behind it..

Answer 46

If you don't want to do it, then do like this:
\[y - 5 = -\frac{2}{3}(x - 6)\]

Multiply -2/3 inside brackets:

\[y - 5 = -\frac{2x}{3} + 4\]

Now bring x on LHS, so add 2x/3

\[y - 5 + \frac{2x}{3} = 4 \implies \frac{2x}{3} + y = 9\]

Got it till here?

Answer 47

OK so 2/3x+y=9
now what?

Answer 48

You will take LCM here or what...

Answer 49

Or here, also time it with 3, so you will easily remove 3 from denominator.. My main purpose is to remove denominator terms, denominator of x and y terms should be 1..

Answer 50

OHHH I think I got it now! Thanks!

Answer 51

You sure??

Answer 52

Finally you get : \(2x + 3y = 27\)

Answer 53

Thanks!