Write the equation of a line that is perpendicular to the line y=1/3x-7 and passes through the point (5,-2)

Slope-intercept form of a line:
y=mx+b
m=slope

other perpendicular line to this line (y=mx+b) will have the next slope:
m´=-1/m

We have this line in slope-intercet form:
y=1/3x-7
m=1/3
A perpendicular line will have the next slope:
m´=-1/m=-1(1/3)=-3

Now, we have a point (5,-2) and the slope (-3).
point-slope form: given a point  (x₀,y₀) and the slope m, the point-slope form will be:

y-y₀=m(x-x₀)

In this case:
y-(-2)=-3(x-5)
y+2=-3x+15
y=-3x+15-2
y=-3x+13

The equation of a line (slope intercept form) that is perpendicular to the line y=1/3x-7 and passes throught the point (5,-2) is:

y=-3x+13