Question

jordan uses a linear equation to model the data in a table. which reasoning might jordan have used in the decision to model the data with a linear equation?

the products of corresponding \\(x\\)- and \\(y\\)-values are equal.
the ratios of consecutive \\(y\\)-values are equal for evenly spaced \\(x\\)-values.
the \\(y\\)-values are the reciprocals of the corresponding \\(x\\)-values.
the change in \\(y\\)-values is constant for evenly spaced \\(x\\)-values.

Explanation:

Analyze linear function characteristics

$$ y = mx + b \implies \Delta y = m \Delta x $$

Evaluate constant rate of change

$$ \Delta x = \text{constant} \implies \Delta y = m \cdot \text{constant} = \text{constant} $$

Match with options

$$ \text{Option 4: "The change in } y\text{-values is constant for evenly spaced } x\text{-values."} $$

Answer:

• The products of corresponding x- and y-values are equal.
• The ratios of consecutive y-values are equal for evenly spaced x-values.
• The y-values are the reciprocals of the corresponding x-values.
• The change in y-values is constant for evenly spaced x-values. (Correct answer)