The slopes of perpendicular lines are negative reciprocals. That means that when you multiply then together, you get -1.
The slopes of all the choices are easy to see because all the choices are in y = mx + b form, slope-intercept form.
If we write our equation in slope-intercept form also, then we can see its slope easily.
We solve -3x + y = 7 for y.
Add 3x to both sides to get
y = 3x + 7
The slope is 3.
We need a negative reciprocal slope to 3, so we need -1/3.
Only choice A has a slope of -1/3.
Answer: Choice A, y = -1/3x + 7