Question

the linear equation that models the height of water in a tank after x minutes is
y - 120 = -2.5(x - 15)
where x represents the minutes since draining began and y represents the height in centimeters.
the key feature that represents the time it takes, in minutes, for the tank to be empty is

the range
the domain
the x-intercept
the y-intercept
the rate of change

which means that it will take the tank

minutes to empty.

Explanation:

Step1: Identify the key feature

To find the time when the tank is empty, we need to find when \( y = 0 \) (height of water is 0). This corresponds to finding the \( x \)-intercept because the \( x \)-intercept is the value of \( x \) when \( y = 0 \).

Step2: Solve for \( x \) when \( y = 0 \)

Start with the equation \( y - 120 = -2.5(x - 15) \).
Substitute \( y = 0 \):
\( 0 - 120 = -2.5(x - 15) \)
Simplify left side: \( -120 = -2.5(x - 15) \)
Divide both sides by -2.5: \( \frac{-120}{-2.5} = x - 15 \)
Calculate \( \frac{-120}{-2.5} = 48 \), so \( 48 = x - 15 \)
Add 15 to both sides: \( x = 48 + 15 = 63 \)

Answer:

The key feature is the \( x \)-intercept, and it will take the tank 63 minutes to empty.