The standard format of a straight line is y = mx+c
m is the slope and c is the y intercept.
So if our line is y = mx+b then it passes through point P (2,3).
When m = 1
3 = 1*2+b
b = 1
So the equation of line is y = x+1
When m = -1
3 = -1*2+b
b = 5
So the equation of line is y = -x+5
When b = 2
3 = m*2+2
m = 1/2
So the equation of line is y = (1/2)x+2
P and having slope m. P(2,3),m=1
Standard form is actually Ax + By + C where A, B, and C are integer coefficients.
Given a point and its slope, its best to use the point slope form which in general terms is y - y1 = m(x - x1) where (x1,y1) is the point and m is the slope.
You can use that to get to standard.
y - 3 = 1(x - 2)
Rearrange to get x and y on the same side:
y - x = 1