Point-slope form is...
You probably already know that m=slope.
I am assuming that x+y=1 is the line at issue. It is in standard form. Standard form is
Ax+By=C, A and B do not equal zero and A is greater than zero.
Let's convert x+y=1 into slope-intercept form of...
y=mx+b, m is slope and b is y-intercept, the value of y when x=0.
The slope is -1.
The slope of the line parallel to this is also -1.
Let's add 3 to both sides so that we may combine like terms of 2 and 3...
The slope perpendicular to -1 is 1. It is the negative inverse. The inverse of 1/1 is 1/1. However, for example, if the slope is -2, the slope of the line perpendicular to this would be 1/2.