Question

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. Select the equation in point-slope form for the line that represents the height of the bucket relative to the top of the well.

Answer 1

Answer:  $y=4x-3$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Let be "y" the height of the bucket relative to the top of the well and "x" the time.

We know that:

- She lifts the bucket of water at a rate of $4\ \frac{ft}{s}$, this means that:

$m=4$

- After 1 second, the bucket is 1 feet below the top of the well. This means that:

When $x=1$, $y=1$

Knowing this, we can substitute the known values into  $y=mx+b$ and solve for "b":

$1=4(1)+b\\\\1-4=b\\\\b=-3$

Therefore, we get that the equation in Slope-Intercept form for the line that represents the height of the bucket relative to the top of the well is:

$y=4x-3$