A water tank is being emptied and replaced with another one

Question

y-axis is water in gallons (0,35)
The x-axis is hours
Points are (0,35),(5,20),(10,5)(11.5,0)
How much water did the tank have when it started being drained ___ this represents the ___ of the line graph
The tank is emptying at a rate of _____ this represents the ___slope

The equation that would represent this scenario would be_____

Answer 1

To analyze the situation with the water tank's draining process, let's address each part of your question step-by-step.

1. Initial Amount of Water: The tank starts with water at the point (0, 35). This means that when \( x = 0 \) (at time 0 hours), the amount of water in the tank was 35 gallons. Therefore, the tank had 35 gallons of water when it started being drained. This represents the y-intercept of the line graph (the value of \( y \) when \( x = 0 \)).

2. Rate of Emptying: To find the rate at which the tank is emptying, we can calculate the slope of the line represented by the points.

   First, we need to determine the change in gallons per hour. We can take two points on the line: (0, 35) and (11.5, 0).

   \[ \text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{0 - 35}{11.5 - 0} = \frac{-35}{11.5} \approx -3.04 \]

   This means the tank is emptying at a rate of approximately 3.04 gallons per hour. This represents the slope of the line.

3. Equation of the Line: The slope-intercept form of a line is given by the equation:

   \[ y = mx + b \]

   Where \( m \) is the slope and \( b \) is the y-intercept. Here, \( m \approx -3.04 \) and \( b = 35 \).

   Therefore, the equation that would represent this scenario would be:

   \[ y = -3.04x + 35 \]

In summary:

• The tank had 35 gallons of water when it started being drained; this represents the y-intercept.
• The tank is emptying at a rate of 3.04 gallons per hour; this represents the slope.
• The equation that would represent this scenario would be \( y = -3.04x + 35 \).

Answer 2

3.04 represents a(an) ______slope

Answer 3

The value of 3.04 represents a negative slope because it indicates that the quantity of water in the tank is decreasing over time as the tank is being emptied. In the context of line graphs, a negative slope signifies a decline in the dependent variable (in this case, the gallons of water) as the independent variable (time in hours) increases.

Thus, the complete statement would be: 3.04 represents a negative slope.