Question

What is the equation of the line passing through (-3,6) and is parallel to the line y=4x-2 in standard form
Choices:
x-4y=-18
x+4y=18
4x-y=-18
4x+y=18

Answer 1

What does it mean, for two lines to be parallel?

Answer 2

yes

Answer 3

My question wasn't a yes-or-no question...

Answer 4

no matter how far they extend, they will never meet

Answer 5

Yeah, actually, that is true... but what does it say about their slopes?

Answer 6

they're equal?

Answer 7

Yup :)
so, what is the slope of
y = 4x - 2 ?

Answer 8

4
--
1 or 4?

Answer 9

Very good...
So, our missing line must also have a slope of 4, to be parallel to y = 4x - 2, correct?

Answer 10

right!

Answer 11

We know the slope of our line, \(\large \color{blue}4\) and we know it passes through the point \(\large (\color{red}{-3 } \ , \ \color{green}6)\)

When we know the slope \(\large \color{blue}m\) of a line and we know it passes through a point \(\large (\color{red}h \ , \ \color{green}k)\)
Then the equation of the line is *always* given by this form:
\[\huge y = \color{blue}mx - \color{blue}m\color{red}h+\color{green}k\]

Answer 12

You know our slope and the point, just plug in :)

Answer 13

so when you plug in would you get
y=4(x)-4(-3)+6 which would simplify to
y=4x+12+6
y=4x+18 ? is this right so far?
so then since it needs to be in standard form (ax+by=c) you would rearrange it to say 4x+y=18 which would be the answer?

Answer 14

@terenzreignz

Answer 15

I don't see how
y = 4x + 18
leads to 4x + y = 18

Answer 16

Oh, I'm probably wrong but I thought you could simply just rearrange the equation around to fit the required formula

Answer 17

yes, in particular, y = 4x + 18
It's the same as
4x + 18 = y
just switch it around...

Answer 18

Now, try arranging that in standard form...

Answer 19

standard form is ax+by=c correct?

Answer 20

Yes...

Answer 21

So the answer in standard form would be 4x+y=18 ?

Answer 22

I see what the problem is :)
You forget that when you transfer terms between equal-signs, you have to CHANGE THE SIGN.
Positive becomes negative, and negative becomes positive :)

Answer 23

Ahhh! So would the left side of the equation remain the same and the positive 18 become -18?

Answer 24

\[\Large x \color{green}{+c}= y\]
If I want to move the c over to the right side, essentially, I'm subtracting it from both sides...
\[\Large x\color{blue}{+c}\color{red}{-c}=y\color{red}{-c}\]
\[\Large x = y\color{red}{-c}\]

Answer 25

Let's start with this...
\[\Large 4x + 18 = y\]

Answer 26

What we want is the x and y on the left side, and the constant, 18, on the right.
How to bring the (positive) y to the left side?

Answer 27

you would need to subtract it, so when it is moved to the left side it would become negative

Answer 28

Yes... so...
\[\Large 4x +18\color{red}{-y }=0\]
Now we want that +18 on the right side... what to do?

Answer 29

subtract it to get it off the left side and onto the right, making it -18 on the right side.

Answer 30

Correct :)
\[\Large 4x -y = \color{blue}{-18}\]
voila :)

Answer 31

Which would make the equation 4x-y=-18, which is in standard form, and the right answer!!!! :D THANK YOU SO SO SO SO SO SO SO SO MUCH!!!!!!!!

Answer 32

The particular skill of transferring terms from one side to another and changing the sign, it's called transposition...
master that, and you'll master lines in no time :)

Great job.
*Almost* perfect.


Perfect it next time, promise me, I know you can do it ^_^

Answer 33

Thank you! :)