**Question:** Which is a table of ordered pairs defined by \( y = \dfrac{2}{7}x + 2 \)? **Answer Choices:** 1. \[ \begin{array}{c|c} x & f(x) \\ \hline -13 & -24 \\ 14 & 46 \\ -14 & 6 \\ 21 & -4 \\ \end{array} \] 2. \[ \begin{array}{c|c} x & f(x) \\ \hline 7 & 0 \\ 14 & -2 \\ -14 & 6 \\ 21 & -4 \\ \end{array} \] 3. \[ \begin{array}{c|c} x & f(x) \\ \hline 7 & 0 \\ 14 & -2 \\ -14 & -24 \\ 21 & -4 \\ \end{array} \] **Explanation:** First, let’s rewrite the equation \( y = \dfrac{2}{7}x + 2 \) in function form: \( f(x) = \dfrac{2}{7}x + 2 \). To find the correct table of ordered pairs, substitute each \(x\) value from the tables into the function to see if \(f(x)\) equals the corresponding \(y\) value. For the first table: 1. For \( x = -13 \): \[ f(-13) = \dfrac{2}{7}(-13) + 2 = -\dfrac{26}{7} + 2 = -\dfrac{26}{7} + \dfrac{14}{7} = -\dfrac{12}{7} \approx -1.71 \neq -24 \] 2. For \( x = 14 \): \[ f(14) = \dfrac{2}{7}(14) + 2 = 4 + 2 = 6 \neq 46 \] 3. For \( x = -14 \): \[ f(-14) = \dfrac{2}{7}(-14) + 2 = -4 + 2 = -2 \neq 6 \] 4. For \( x = 21 \ The image displays two tables of values representing functions \( f(x) \) for different input values of \( x \). Here's the detailed transcription: ### Table 1 This table shows the values of \( f(x) \) for given \( x \) values: | \( x \) | \( f(x) \) | |:-------:|:---------:| | 8 | 18 | | 14 | 18 | | -14 | 6 | | 21 | 46 | ### Table 2 This table presents another set of values of \( f(x) \) for different \( x \) values: | \( x \) | \( f(x) \) | |:-------:|:---------:| | 15 | 32 | | 14 | -24 | | -14 | 6 | | 22 | -4 | Explanation: - Each table consists of two columns: one for the input value \( x \) and one for the corresponding output value \( f(x) \). - In the first table, the function \( f(x) \) maps: - \( x = 8 \) to \( f(x) = 18 \) - \( x = 14 \) to \( f(x) = 18 \) - \( x = -14 \) to \( f(x) = 6 \) - \( x = 21 \) to \( f(x) = 46 \) - In the second table, the function \( f(x) \) maps: - \( x = 15 \) to \( f(x) = 32 \) - \( x = 14 \) to \( f(x) = -24 \) - \( x = -14 \) to \( f(x) = 6 \) - \( x = 22 \) to \( f(x) = -4 \) These tables can be used to understand the different outputs of the same or different functions for various input values of \( x \).