Question

Some of the water features at sapphire island are periodically treated with a chemical that prevents algae growth. The directions for the chemical say to add 16 fluid ounces per 10,000 gallons of water. Make a table that showed how much of the chemical to add for water features that hold 10,000 ,20,000 ,30,000 ,40,000; and 50,00 gallons of water.

Chart:
16 -->10,000 gallons
32 -->20,000 gallons
48 -->30,000 gallons
64 -->40,000 gallons
80 -->50,000 gallons

Now what is a linear equation in two variables that models the situation. Tell what each variable in the equation represents

Answer 1

As the problem mentions, the mass of fluid added is dependent on the volume of the water. So this means that the independent variable is the volume, and the dependent variable is the ounces of fluid. When you graph the linear equation, the independent variable is along the x-axis and the dependent variable is along the y-axis. So, you actually assign x to ounce of fluid added and y to the volume of water.

Now, we construct the linear equation using the slope-intercept form. Its equation is: y = mx + b, where m is the slope and b is the y-intercept. We can find the slope from at least two given data points. The equation would be

m = (y₂ - y₁) / (x₂ - x₁)

Let's choose two random points: Point 1 (10,000,16) and Point 2 (20,000,32). Note that the points should be written in (x.y) form. So, the slope of the line is equal to:

m = (32 - 16) / (20,000 - 10,000)
m = 1/625

So, the equation is y = x/625 + b. Now, we can determine b by using any point. Suppose we use the third data point, P(30,000, 48). Substitute this to x and y.

48 = 30,000/625 + b
b = 0

Therefore, the linear equation is: y = x/625. The variable y represents the volume of the water in gallons, and the variable x is the mass of fluid added in ounces.