By rearranging the equation, the slope can be directly read from it.
You said -x + 1/3 y = 5
Add 'x' to each side: 1/3 y = x + 5
Multiply each side by 3: y = 3x + 15
This form of the equation is the so-called "slope / intercept form",
because the numbers on the right side are the slope and intercept
of its graph.
When the equation is graphed, the y-intercept of the line is 15,
and the slope of the line is 3 y-units per x-unit.