We are asked to find the linear function that represents the amount of water in inches w in a bucket after t minutes. The desired linear function has to follow a specific format.
y= m x+ b
In this case, y is represented by w and x is represented by t.
w= m t+ b
For an equation in this form, m is the slope and b is the y-intercept. To find the desired linear function we will calculate the slope and the y-intercept. We can do this by using any two points lying on the line that is the graph of the linear function. Let's go through the content of the exercise and get the points we need!
Sentence From the Exercise
Point (t,w)
At time t= 0, water begins to drip out of a pipe into an empty bucket.
( 0, 0)
After 56 minutes, 8 inches of water are in the bucket.
( 56, 8)
Now we can use the obtained points to calculate m. We will start by substituting the points into the Slope Formula.
In our function, a slope of 17 means that after every minute the amount of water in the bucket increases by 17 inches. Now that we know the slope, we can write a partial version of the equation.
w= 1/7 t+ b
To complete the equation, we also need to determine the y-intercept b. Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 0, 0).
