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 slope-intercept 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 slope-intercept form of the line that represents the height of the bucket over time, we start with the information given:

1. Isobel lifts the bucket at a rate of 4 ft/s, which gives us the slope (m) of the line as 4.
2. After 1 second (x = 1), the bucket is 1 ft below the top of the well, meaning the height (y) is -1 ft.

Now we can use the slope-intercept form, which is ( y = mx + b ).

Since we know the slope ( m = 4 ), we need to find ( b ) (the y-intercept). We can use the point (1, -1) we have:

1. Plugging into the equation:

(-1 = 4(1) + b)

(-1 = 4 + b)

(b = -1 – 4)

(b = -5)

Now we can write the equation:

So, the equation is:

y = 4x – 5

In summary, the final answer in the requested form is:

y = 4x – 5