Q:

# Suppose someone opens the valve on a large water tank so that water drains out. Choose a starting volume of water in the tank (from 100 to 500 gallons), and choose how much water drains out each day (from 2 to 5 gallons). Write the equation that models the relationship between time (x) and water volume (y) in slope-intercept form. Post your equation. Choose another equation from the discussion board and answer the following. Write the equation in slope-intercept form, and use the equation to find the amount of water in the tank exactly 2 days after the valve is opened. Determine the slope of the line. Describe the meaning of the slope in this context. Rewrite the equation in standard form, and use that equation to find the x- and y-intercepts. Describe the meaning of each intercept. Do these equations represent an exact or approximate relationship between time and volume? This could be a matter of opinion. What is your opinion? Explain.

Accepted Solution

A:
Answer:Let amount of water in tank  =y(100≤y≤500)Amount of water drained in a day = c [2≤c≤5]Time =x [1≤x≤ number of days till water in the tank drains out]So Equation that models the relationship between time (x) and water volume (y) in slope-intercept form=y =  m x+ c, If x=0, y=400 gallon,and if x=1 day then y=396This is a linear graph.$$\frac{y-400}{x-0}=\frac{400-396}{0-1}\\y-400=-4x\\y=-4x+400$$Amount of water in the tank after 2 days =y=-4×2+400=-8+400=392 Here ,m = -[amount of water drained in a day]= -c= -4$$y=-4x+400\\4x+y=400\\\frac{x}{100}+\frac{y}{400}=1$$x-intercept=100, y-intercept=400Y intercept shows amount of water in the beginning.As we can see that as time increases volume of water in the tank decreases.So linear equation of two variable  completely or exactly satisfies the relationship between time and volume.If we divide y intercept by x intercept i.e amount of water tank has by x intercept we get amount of water draining in a day.