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.
My equation. Y=500-5x
I don't know what to do after this??
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.
pkjumuii
To proceed from the given equation, we will first rewrite it in slope-intercept form, which is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Given equation: y = 500 - 5x
To rewrite it in slope-intercept form, we express it as: y = -5x + 500
Now, we can use this equation to find the amount of water in the tank exactly 2 days after the valve is opened. To do this, we substitute x = 2 into the equation and solve for y.
y = -5(2) + 500
y = -10 + 500
y = 490
Therefore, 2 days after the valve is opened, there will be 490 gallons of water in the tank.
The slope of the line in this context is -5. In this equation, the slope represents the rate at which the water volume decreases each day. Since the coefficient of x is negative, it indicates that for every one day that passes, the water volume decreases by 5 gallons.
To rewrite the equation in standard form, we will move the variables to one side and the constant term to the other side of the equation. The equation will be in the form Ax + By = C, where A, B, and C are constants.
Given equation: y = -5x + 500
Rearranging the terms, we get:
5x + y = 500
In this equation, the x-intercept represents the amount of time it takes for the water volume to reach zero. To find the x-intercept, we set y = 0 and solve for x.
5x + 0 = 500
5x = 500
x = 100
Therefore, the x-intercept is 100, which means it would take 100 days for the water volume to reach zero.
The y-intercept of the equation represents the initial volume of water in the tank when x = 0. In this case, the y-intercept is 500 gallons, which means there are initially 500 gallons of water in the tank when the valve is opened.
Regarding the exactness or approximation of the relationship between time and volume, this is a matter of interpretation. The given equation assumes a fixed daily drainage rate without accounting for any external factors that could influence the rate of water drainage. Hence, it can be seen as an approximate relationship based on this simplified model.