To describe the relationship between the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] from the given table, we can derive a linear equation of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
The table of data points is:
[tex]\[
\begin{array}{c|r}
x & y \\
\hline
0 & -6 \\
1 & 1 \\
2 & 8 \\
3 & 15 \\
4 & 22 \\
5 & 29 \\
\end{array}
\][/tex]
Based on the calculations, the slope ([tex]\( m \)[/tex]) and intercept ([tex]\( b \)[/tex]) for the linear relationship are:
[tex]\[
m = 7 \quad \text{and} \quad b = -6
\][/tex]
Thus, the complete linear equation that describes the given relationship is:
[tex]\[
y = 7x - 6
\][/tex]
So, the final equation for [tex]\( y \)[/tex] is:
[tex]\[
y = 7x + (-6)
\][/tex]
In the standard form, it is written as:
[tex]\[
y = 7x - 6
\][/tex]
