
slope point equation
This should be easy. This is first time I'm doing these in over a decade.
Write the equation of the line that goes through point P and has slope m.
P(5,2), m = 1
Here is what I did:
Y – y1 = m( x – x1)
Y – 2 = 1(x – (5))
Y – 2 = x + 5
Y = x + 7
X + y = 7
Here is what the answer is supposed to be:
x + y = 3
how did I screw this up? Thank you.

There's a mistake going from line 2 to 3 on the righthand side. The x  (5) becomes x + 5, but when you distribute the 1, you get x  5.
I find that there's an easier way to do these sorts of problems:
We know the slope is 1 so let's pretend the equation of the line is y = x. We want it to run through (5, 2), so we plug in 5 for x. y = 5 then. So we are 3 units above our goal, which is 2. So we need to come down 3. Thus, the equation is actually y = x  3.

