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.

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 =

m = 1/3  and we know y intercept b =0

So equation becomes

Function

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

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

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

he kicked it up? is this the answer ?

step-by-step explanation: