Question

The water level in Noah's water tank is 72 inches high. Noah begins to drain a water tank by opening a valve. The water drains at a speed up 5 inches per minute. Write an equation for slope.

Answer 1

An equation of slope:

y = -5x+72

Explanation:

The equation of slope intercept is given by:

`y=mx+c` where m is the slope and c is the y-intercept or initial value.

Let x represents the time in minutes and y represents the height of the water level

As per the statement:

The water level in Noah's water tank is 72 inches high.

At x = 0

y= 72

It is also given that:

The water drains at a speed up 5 inches per minute.

Here, m represent the slope in inches per minute

`m = -5` (as the water drains)

Substitute in [1] we get;

y = -5x+c

Substitute x = 0 then;

72 = -5(0)+c

72 = c

⇒equation becomes: y = -5x+72

Therefore, an equation of slope is y = -5x+72

Answer 2

Answer: The required equation of slope is given by

`y=72-5x`

Explanation:

Since we have given that

Length of the water level in Noah's water tank = 72 inches

Speed at which water drains = 5 inches per minute

Let the height of the tank be y.

Let the number of minutes be x.

So, the equation of slope is given by

`y=72-5x`

which represents the height of water level of 72 inches is reduced by 5x inches as

`Distance=Speed* Time\\\\Distance=5* x\\\\Distance=5x`

Hence, the required equation of slope is given by

`y=72-5x`