Question

water from a leaking faucet is dripping into a cylindrical cup. the height of water in inches, \\(y\\), after \\(x\\) hours is graphed below.

Explanation:

Identify the given points on the graph

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK0
$$

Calculate the rate of change (slope)

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Determine the linear equation

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK2
$$

Answer:

The graph shows a linear relationship between the time in hours, \(x\), and the height of the water in inches, \(y\).

By identifying the points plotted on the line:

• At \(1\) hour, the height is \(2\) inches: \((1, 2)\)
• At \(2\) hours, the height is \(4.1\) inches: \((2, 4.1)\)
• At \(3\) hours, the height is \(6.2\) inches: \((3, 6.2)\)
• At \(4\) hours, the height is \(8.2\) inches: \((4, 8.2)\)
• At \(5\) hours, the height is \(10.2\) inches: \((5, 10.2)\)

The rate of change (slope) is approximately \(2\) inches per hour, which gives the linear equation:

$$y = 2x$$

(or more precisely, \(y = 2.05x\) using the plotted points).