BThe variable x represents the minutes after the cleaning begins.
CThe variable y is the amount of carpet cleaner in the tank.
Ay=- 4x +128
B128 fluid ounces
C32 minutes
Practice makes perfect
We are given a table that shows the amount y in fluid ounces of carpet cleaner in a tank after x minutes of cleaning.
x
y
5
108
10
88
15
68
We want write an equation that represents the amount of cleaner in the tank after x minutes. To do so, remember that equations written in point-slope form follow a specific format.
y- y_1= m(x- x_1)
In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. Consider that the line passes through the given three points. To determine the slope of the line, we use the slope formula. Let's substitute two of the points given on the table, (5,108) and (10,88), into the slope formula to calculate m.
Now that we know that the slope of the line is - 4, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 15, 68).
Please note that any point on the line can be used to form a point-slope equation. Therefore, our equation is only one of infinitely many possible equations!
Let's recall the equation obtained in Part A.
y= - 4x+128
To calculate the amount of cleaner when the cleaning begins remember that x represents the number of minutes, which means that initial time will occur when x=0. Let's substitute this into the above equation and calculate the amount of cleaner.
Therefore, there is 128 fluid ounces of carpet cleaner when the cleaning begins.
To calculate when the tank will be empty, we need to solve the equation obtained in Part A.
y= - 4x+128
Since the tank will be empty, the amount of cleaner will be equal to zero. Then, we need to substitute y=0 into the above equation and solve it for x. Let's do it!
