How to find the equation of a line using only two coordinates?

Question

anonymous · Answer

1. Determine the equation of the line, in standard form, that will get your spacecraft from the Launch Area to Point A.

Launch Area:_(1, 2)_ 
Point A:_(6,7)_


Using these points, what would I need to do in order to answer the question? I'm not looking for answer more-so than I am trying to figure out how to do this. Thanks :)

anonymous · Answer

If anyone could provide basic steps as to what to do, even that would help a ton. :)

anonymous · Answer

First find slope.
$$\frac{ y _{1}-y _{2} }{ x _{1} -x _{2} }$$
After you find slope we will use the equation
$$y-y _{1}=m(x-x _{1})$$

anonymous · Answer

Make sense?

anonymous · Answer

Looks familiar enough, glad to know I was somewhat on the right path haha. I'll work it out and see what happens :)

anonymous · Answer

Okay, if you feel uncertain feel free to post your work.

anonymous · Answer

7-2 divided by 6-1 = 5/5 slope

Plugging it in and converting it to standard form:
y -2=5/5(x-1)
y-2=5/5x-5/5
  +2           +2

    y=       5/5x-3/5
-5/5x    -5/5x

-5/5x + y = -3/5
x5       x5       x5

-5x + 5y = -3


My only question was on step 3 (when I added 2 to both sides), did I properly add it to the right side (I went from 5/5x - 5/5 *~to~* 5/5x -3/5)?

@RoseDryer

anonymous · Answer

Well since your slope is 5/5 that equals 1
So
y - 2=1(x-1)
y - 2 = x - 1
   +2     +2
 y=  x + 1
-x     -x

-x + y = 1

anonymous · Answer

Woah, looks like I'm way off. Let me try reworking it :)

anonymous · Answer

y-y1=m(x-x1)
y-2=1(x-1)
y-2=1x+1
-1x -1x
-1x + y = 1

How's that look?

anonymous · Answer

@RoseDryer Not sure if I should mention you or not lol.

anonymous · Answer

That's correct but you don't need the 1 in front of the x but you do keep the negative.