Consider the given equation of a line.
y=- x+1 ⇔ y= - 1x+ 1
When lines are parallel, they have the same slope. With this, we know that all lines that are parallel to our given line will have the same slope of - 1. Knowing this, we can write a general equation in slope-intercept form for all the lines parallel to the given line.
y= -x+ b
In addition to being parallel, we need a line that passes through the point ( 4, 4). By substituting this point into the general equation for x and y, we will be able to solve for the y-intercept b of the parallel line.
