Final answer:
The equation of the line that passes through the point (5, -5) with a slope of -1/5 is y = -1/5x - 4.
Step-by-step explanation:
The equation of a line can be determined using the point-slope form, which is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
In this case, the given point is (5, -5) and the slope is -1/5.
Plugging these values into the point-slope form, we get: y - (-5) = -1/5(x - 5)
Simplifying, the equation becomes: y + 5 = -1/5(x - 5)
Expanding and rearranging the equation, we get: y = -1/5x + 1 - 5, which simplifies to y = -1/5x - 4.
Therefore, the equation of the line that passes through the point (5, -5) and has a slope of -1/5 is y = -1/5x - 4.