Ageometry class is asked to find the equation of a line that is parallel to y – 3 = −(x + 1) and passes through (4, 2). trish states that the parallel line is y – 2 = –1(x – 4). demetri states that the parallel line is y = –x + 6.

A paralell line has same slope

the equation of a line with slope of m and passing through point (x1,y1) is
y-y1=m(x-x1)

we are given
y-3=-1(x+1)
slope=-1
we don't need the point

we want it to pass through (4,2)
x1=4
y1=2

y-2=-1(x-4)
trish is right
solve for y

y-2=-x+4
y=-x+6

both are correct

Fis the domain that we’ll make it better