what is an equation of the line that passes through the point (5,1) and is parallel to the line x+y=9

Y=9-x is slope-intercept form of that line, which means it has a slope of -1. Parallel lines have the same slope, so the slope of this new line will also be -1.

To find the line that goes through (5,1), we can use a blank equation y=mx+b. We know that m=-1, so we can use the given point to find b:

y=mx+b
Y=-x+b
1=-5+b
6=b

So the line would be y=-x+6.