Isobel is pulling water up from an old-fashioned well. She lifts the bucket of water at a rate of 4 ft/s, and after 1 s, the bucket is 1 ft below the top of the well. What is the equation in point-slope form of the line, where y represents the height, in feet, of the bucket relative to the top of the well after x seconds? y + ___ = ___ (x + ___)

To find the equation in point-slope form of the line, we can start by determining the initial conditions and the slope of the line.

1. Initial Condition: After 1 second, the bucket is 1 ft below the top of the well, meaning its height is -1 ft relative to the top of the well. So, when ( x = 1 ), ( y = -1 ).

2. Rate of Change (Slope): Isobel is pulling the bucket up at a rate of 4 ft/s. This means the slope ( m ) is 4.

Using the point-slope form of the equation, which is given by:

[

y – y_1 = m(x – x_1)

]

We can substitute ( y_1 = -1 ), ( m = 4 ), and ( x_1 = 1 ):

[

y – (-1) = 4(x – 1)

]

This simplifies to:

[

y + 1 = 4(x – 1)

]

In point-slope form, the equation is:

[

y + 1 = 4(x – 1)

]

So, filling in the blanks, we have:

y + 1 = 4 (x + -1)

This shows the relationship between the height of the bucket and time.