Question

Isabel 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 that represents the height of the bucket relative to the top of the well?

Answer 1

Answer:

The equation in point-slope form of the line that represents the height of the bucket relative to the top of the well is $y + 1 = 4\cdot (t-1)$.

Step-by-step explanation:

The point-slope form of the equation of the line is represented by the following expression:

$y - y_{o} = m\cdot (t-t_{o})$ (1)

Where:

$t$ - Time, measured in seconds.

$y$ - Height below the top of the well, measured in feet.

$t_{o}$, $y_{o}$ - Known information of the well, measured in seconds and feet, respectively.

$m$ - Slope, measured in feet per second.

If we know that $(t_{o},y_{o}) = \left( 1\,s, -1\,ft\right)$ and $m = 4\,\frac{ft}{s}$, then the equation in point-slope form of the line is:

$y + 1 = 4\cdot (t-1)$

The equation in point-slope form of the line that represents the height of the bucket relative to the top of the well is $y + 1 = 4\cdot (t-1)$.