Final answer:
To represent the depth of the water y after x minutes, we can use the equation y = -0.2x + 48. This equation assumes a constant rate of change in water depth over time, calculated from two given measurements at 12:15 p.m. and 12:35 p.m.
Step-by-step explanation:
To find an equation that represents y, the depth of the water (in inches), after x minutes, we need two data points to determine the rate at which the water is decreasing.
We know that at 12:15 p.m. the water was 45 inches deep, and then at 12:35 p.m., it was 41 inches deep.
So in 20 minutes, the water level dropped by 4 inches. We will assume the rate of change in water level is constant.
First, calculate the rate of change per minute which is the slope (m):
Slope (m) = (Change in depth) / (Change in time) = (41 - 45) inches / (12:35 - 12:15) minutes = -4 inches / 20 minutes = -0.2 inches/minute.
We can now establish the point-slope form of the line using the point (15, 45) since 12:15 p.m. corresponds to 15 minutes after noon:
y - y1 = m(x - x1)
Where y1 is 45 and x1 is 15. Plugging the values in, we get:
y - 45 = -0.2(x - 15)
Rewriting in slope-intercept form:
y = -0.2x + 48
So the equation that represents the depth of the water y in inches after x minutes is y = -0.2x + 48.