Final answer:
The distance between the two parallel lines is 10 units, calculated by finding the difference between their y-intercepts.
Step-by-step explanation:
The distance between the two lines y = -(1/3)x+7 and y = -(1/3)x-3 can be calculated by examining the difference in their y-intercepts. As both lines have the same slope, -1/3, they are parallel and will never intersect. The distance between two parallel lines is constant anywhere along the lines, and can be determined by the vertical distance between the y-intercepts.
To find this distance, we subtract the lesser intercept (-3) from the greater one (7):
Distance = 7 - (-3) = 7 + 3 = 10 units.
This distance is irrespective of the x-values since both lines are parallel and maintain a consistent distance from each other.