Question

The equation y = −3x + 7 represents the amount of water y left in a 7-gallon tub after x minutes.

Part A

Where does the graph of the equation intersect the y-axis and the x-axis?

y-axis: (
,
)

x-axis: (
,
)

Part B

What do these points represent?

At
3
minutes, the tub has
7
gallons of water.

The tub is empty at
minutes.

Answer 1

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.