QuestionMatch each table of data on the left with its equation on the right and briefly explain why it matches the data. Homework Helps a. \begin{tabular}{|c|c|c|c|c|c|c|} \hline$x$ & 1 & 0 & -4 & 2 & -2 & -1 \\ \hline$y$ & 4 & 3 & -1 & 5 & 1 & 2 \\ \hline \end{tabular} (1) $y=x$ (2) $y=3 x-1$ (3) $y=x+3$ b. \begin{tabular}{|c|c|c|c|c|c|c|} \hline$x$ & -1 & 3 & 1 & 0 & -2 & 2 \\ \hline$y$ & -1 & -9 & -1 & 0 & -4 & -4 \\ \hline \end{tabular} (4) $y$ A= $x^{2}$ (5) $y=-x^{2}$ c. \begin{tabular}{|c|c|c|c|c|c|c|} \hline$x$ & 3 & -2 & 1 & 0 & 2 & -3 \\ \hline$y$ & 12 & 7 & 4 & 3 & 7 & 12 \\ \hline \end{tabular} d. \begin{tabular}{|c|c|c|c|c|c|c|} \hline$x$ & -3 & 4 & 2 & -2 & 0 & -10 \\ \hline$y$ & -10 & 11 & 5 & -7 & -1 & -31 \\ \hline \end{tabular}

Studdy Solution
For table (d), check the equation $y = 3x - 1$.
Calculate $y$ for each $x$: $\begin{aligned} &x = -3, \quad y = 3(-3) - 1 = -10, \\ &x = 4, \quad y = 3(4) - 1 = 11, \\ &x = 2, \quad y = 3(2) - 1 = 5, \\ &x = -2, \quad y = 3(-2) - 1 = -7, \\ &x = 0, \quad y = 3(0) - 1 = -1, \\ &x = -10, \quad y = 3(-10) - 1 = -31. \end{aligned}$
Compare these values with the given table: \begin{tabular}{|c|c|c|c|c|c|c|} \hline$x$ & -3 & 4 & 2 & -2 & 0 & -10 \\ \hline$y$ & -10 & 11 & 5 & -7 & -1 & -31 \\ \hline \end{tabular}
Since the values match, the correct equation for table (d) is $y = 3x - 1$.
$\boxed{\text{The correct matches are:}}$
$\begin{aligned} &\text{Table (a) : } y = x + 3, \\ &\text{Table (b) : } y = -x^2, \\ &\text{Table (c) : } \text{None of the given equations match}, \\ &\text{Table (d) : } y = 3x - 1. \end{aligned}$