Find the standard form of the equation of the line.

Question

anonymous · Answer

27) (2,5) (5,7)

misty1212 · Answer

is it as easy as the last one?

misty1212 · Answer

oh no it is not
did you get the slope?

anonymous · Answer

Yes. The slope is 2/3.

anonymous · Answer

I know I use this formula. Y=mx+b

misty1212 · Answer

ok then use the point slope formula
pick a point

anonymous · Answer

Okay. (2,5).

misty1212 · Answer

no dear we are not going to use that, we are going to so something else 
pick a point from the two you have

anonymous · Answer

Oh. Okay!

misty1212 · Answer

ok now write 
$$y-y_1=m(x-x_1)$$ with $$x_1=2,y_1=5,m=\frac{3}{2}$$

misty1212 · Answer

oops i meant $m=\frac{2}{3}$

misty1212 · Answer

you should be looking at $$y-5=\frac{2}{3}(x-2)$$ right?

anonymous · Answer

i already did that and got y=(2/3)x+(11/3)

misty1212 · Answer

now if you were going to write this in "point slope" form you would solve for $y$ but you want "standard form"
$$ax+by=c$$

anonymous · Answer

Oh.

misty1212 · Answer

yeah but you went too far
you got it in slope intercept form
you were asked for standard form

misty1212 · Answer

lets start here $$y-5=\frac{2}{3}(x-2)$$ it i easier

misty1212 · Answer

multiply both sides by $3$ to get 
$$3y-15=2(x-2)$$

misty1212 · Answer

notice of course you have to multiply both sides by 3

misty1212 · Answer

then distribute 
$$3y-15=2x-4$$

misty1212 · Answer

put all the variables on one side, numbers on the other get 
$$3y-2x=11$$ or 
$$2x-3y=-11$$ that is "standard form"

anonymous · Answer

You're right! Gosh, I thought I didn't take it far enough but I went way too far. Thank you again, Misty!

misty1212 · Answer

$$\color\magenta\heartsuit$$