Question

consider the data in the table shown. select all the descriptions that apply.

x	y
1	1
4	4

• the rate of change is 3.
• the rate of change is 1.
• the data represents a linear relationship.
• the data represents a nonlinear relationship.
• the data has a non - constant rate of change.

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate rate between (0,0) and (1,1)

Using the formula, \(\frac{1 - 0}{1 - 0}=\frac{1}{1} = 1\).

Step3: Calculate rate between (1,1) and (4,4)

\(\frac{4 - 1}{4 - 1}=\frac{3}{3}=1\).

Step4: Analyze linearity

Since the rate of change is constant (1) between all pairs of points, the relationship is linear.

Step5: Evaluate each option

• "The rate of change is 3": False, rate is 1.
• "The rate of change is 1": True, as calculated.
• "The data represents a linear relationship": True, constant rate.
• "The data represents a nonlinear relationship": False, it's linear.
• "The data has a non - constant rate of change": False, rate is constant (1).

Answer:

The rate of change is 1, The data represents a linear relationship