Write in point-slope form a line that is parallel to $-4x + 6y = 36$ passing thru $2, 3$

Question

nnesha · Answer

what is the slope of this line -4x+6y=36 ?

calculusxy · Answer

I got $\large \frac{2}{3}$ but I am pretty sure that's wrong.

anonymous · Answer

must be a math teacher made up this question $$-4x+6y=36$$ is the same as $$-2x+3y=18$$

anonymous · Answer

and yes, it is $\frac{2}{3}$

calculusxy · Answer

I know that parallel lines have the same slope?

nnesha · Answer

looks good.
y=mx+b is a slope intercept form where m is slope and b is y-intercept 

and parallel lines have the same slope

nnesha · Answer

correct.
 $$\huge\rm y-y_1=m(x-x_1)$$ point slope from 
m=slope and passes through (x_1,y_1) point

calculusxy · Answer

I don't know why, but my paper says that the formula for the point-slope from is 
$$\large y_1 - y_2 = m(x_1 - x_2) $$

nnesha · Answer

that's the same thing. 
then it's passes through (x_2 ,y_2)

calculusxy · Answer

Okay so do I make up another coordinate by using the slope?

nnesha · Answer

no to write it in point slope form you just one coordinate and slope that's it

nnesha · Answer

need**

calculusxy · Answer

How's that possible can you show me?

nnesha · Answer

it should look like this $$\rm y-9=3(x-34)$$

calculusxy · Answer

Where did you get those numbers from?

nnesha · Answer

we should keep the x_1 and y_1 
and replace 2nd (x_2 ,y_2)  with the given point

nnesha · Answer

that's an example .. :D

calculusxy · Answer

oh okay

calculusxy · Answer

So would we have :
$$\large y - 3 = \frac{ 2 }{ 3 }(x - 2)$$

nnesha · Answer

perfect!

calculusxy · Answer

Thank you!

nnesha · Answer

yw

calculusxy · Answer

Also I have another question. If we have a perpendicular slope then it means that we take the slope of the current line and find the negative reciprocal?

calculusxy · Answer

$$-3 \rightarrow \frac{ 1 }{ 3 }$$ 
Would this work if we have a negative slope?

nnesha · Answer

remember if  one of the coordinate is negative  
lets say we have (-3,-4)
then $$y-(-4)=4(x-(-3)) \large\rm \rightarrow  y+4=4(x+3)$$
you should multiply by the negative sign in the formula

nnesha · Answer

that's correct!

calculusxy · Answer

Thank you SOOOO MUCH! You're the best as always :)

nnesha · Answer

glad to help!
and thanks! o^_^o