Question

the table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. what is the rate of change?

\

$$\begin{tabular}{|c|c|} \\hline \\multicolumn{2}{|c|}{\\text{snowfall amount}} \\\\ \\hline \\text{length of snowfall (hours)} & \\text{amount of snow on the ground (inches)} \\\\ \\hline 0 & 3.30 \\\\ \\hline 0.5 & 4.5 \\\\ \\hline 1.0 & 5.7 \\\\ \\hline 1.5 & 6.9 \\\\ \\hline 2.0 & 8.1 \\\\ \\hline \\end{tabular}$$

a 1.2 inches per hour
b 2.4 inches per hour
c 3.3 inches per hour

Explanation:

🆕 New Concept Discovered: Rate of Change
How fast one quantity changes compared to another.

Step 1: Identify two points from the table

To find the rate of change of a linear function, we can choose any two points from the table in the form \((x, y)\), where \(x\) represents the length of snowfall (hours) and \(y\) represents the amount of snow on the ground (inches).

Let's choose:

• Point 1: \((x_1, y_1) = (1.0, 5.7)\)
• Point 2: \((x_2, y_2) = (2.0, 8.1)\)

Step 2: Apply the rate of change formula

The rate of change (slope) is the change in the dependent variable (\(y\)) divided by the change in the independent variable (\(x\)):

$$\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}$$

Substitute the chosen points into the formula:

$$\text{Rate of Change} = \frac{8.1 - 5.7}{2.0 - 1.0}$$

Step 3: Calculate the final value

Subtract the values in the numerator and denominator:

$$\text{Rate of Change} = \frac{2.4}{1.0} = 2.4\text{ inches per hour}$$

Answer:

B 2.4 inches per hour