Step-by-step 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 = [tex]\frac{gallons}{second} = \frac{1}{3}[/tex]
m = 1/3 and we know y intercept b =0
So equation becomes
[tex]y=\frac{1}{3}x +0[/tex]
Function [tex]f(x)=\frac{1}{3}x[/tex]
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
[tex]18=\frac{1}{3}x +0[/tex]
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
