Answer:
x = 7/3
Explanation:
Part A:
The graph of the equation y = -3x + 7 intersects the y-axis at the point (0, 7). This is because when x = 0, the equation simplifies to y = 7, indicating that there are 7 gallons of water left in the tub at the start.
The graph intersects the x-axis when y = 0. To find this point, we set y = 0 in the equation and solve for x:
0 = -3x + 7
3x = 7
x = 7/3
Therefore, the graph intersects the x-axis at the point (7/3, 0).
Part B:
The point (0, 7) represents the initial amount of water in the tub. When x = 0 (at the start), the equation tells us that there are 7 gallons of water remaining.
The point (7/3, 0) represents the time it takes for the tub to empty. When y = 0, it means that there is no water left in the tub. Solving the equation -3x + 7 = 0, we find that x = 7/3, indicating that it takes 7/3 minutes (or 2 and 1/3 minutes) for the tub to empty.
So, at 3 minutes, the tub has 7 gallons of water, and the tub is empty at 7/3 minutes.