Question

Sophia is filling her bathtub up with water for a bath. The volume of water, y, in gallons, in the tub is a linear function of the number of minutes, x, that have passed since the tank started filling with water. The tub holds 18 gallons of water ad fills at a rate of 1 gallon for every 3 seconds. Graph this function.

Answer 1

Explanation:

The tub holds 18 gallons of water ad fills at a rate of 1 gallon for every 3 seconds.

x is the number of minutes and y is the volume of water

When x=0 then volume of water y =0

so y intercept is 0

We use linear equation y = mx +b where m is the slope and b is the y intercept

Tank fills at a rate of 1 gallon for every 3 seconds.

So slope =
`(gallons)/(second) = (1)/(3)`

m = 1/3 and we know y intercept b =0

So equation becomes

`y=(1)/(3)x +0`

Function
`f(x)=(1)/(3)x`

When x =0 , y=0 we got already (0,0)

Tub holds 18 gallons of water

Now we need to find out number of minutes x takes to fill 18 gallons of water

plug in 18 for y and solve for x

`18=(1)/(3)x +0`

multiply by 3 on both sides

x= 54 seconds to fill 18 gallons of water

other point is (54,18)

Now we use (0,0) and (54,18) to graph the function

The graph is attached below