Question

Indicate the equation of the given line in standard form.
The line that contains the point Q( 1, -2) and is parallel to the line whose equation is...
y - 4 = 2/3 (x - 3)
Anyone know how to solve this??

Answer 1

what do you know about the sloeps of parallel lines?

Answer 2

slopes*

Answer 3

aren't they the same?

Answer 4

correct. and so the slope of our line is the same slope as the given line

Answer 5

So, it is 2/3 ?

Answer 6

correct. now since we'd have to use point-slope form, we need one other piece of information
\(y-y_1=m(x-x_1)\)

Answer 7

I'm not sure what it is.

Answer 8

(x1,y1) is the point the line goes through
m is the slope of the line

Answer 9

we found m

Answer 10

oh, so (1,-2) ?

Answer 11

correct.
\(y-y_1=\dfrac{2}{3}(x-x_1)\)

Answer 12

so, the equation would look like this?
-2-4= 2/3 (1-3)

Answer 13

oh no, we're only replacing x1 and y1

Answer 14

the only information we needed from the other equation was the slope

Answer 15

\((x_1,y_1) = Q( 1, -2) \)
m=2/3

Answer 16

okay, i'm lost again. haha so how do we solve that?

Answer 17

lemme try some color coding

Answer 18

\(y-\color{red}{y_1}=\color{pink}m(x-\color{blue}{x_1})\)

\(y - 4 = \color{pink}{\dfrac{2}{3}}(x - 3)\)

passes through point \(Q( \color{blue}{1}, \color{red}{-2}) \)

Answer 19

It makes some sense but i'm not sure how to solve it now

Answer 20

you just plug and simplify into y=mx+b form

pretend it's one of those kindergarten toys where the red shape goes in the red hole

Answer 21

y- (-2)= 2/3 (x-1) ?

Answer 22

yeah. start with the left hand side
simplify y--2

Answer 23

I got y= 2/3x-8/3
when I put it into standard form I got 2x-3y= 8
Which fits into my answer box online

Answer 24

why'd you put it in standard form?

Answer 25

that's what the question said to do

Answer 26

oh I didn't read the first line, give me a moment

Answer 27

it said I got it right so thank you! you helped me pass (:

Answer 28

y- (-2)= 2/3 (x-1) ?
y+2=2/3x-2/3, subtract 6/3 (2) from both sides
y=2/3x-8/3

Answer 29

awesome

Answer 30

i just googled how to convert to standard form for completion's sake

y=2/3x-8/3

3y=3(2/3x-8/3)

3y=2x-8
2x-3y=8

good job

Answer 31

Thank you! and thanks for the help also

Answer 32

anytime, yo. tag me in the future if it takes a while to get an answer