To describe the relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex], we need to determine the equation of the form [tex]\( y = mx + b \)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
Given data points:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-3 & 13 \\
\hline
-2 & 8 \\
\hline
-1 & 3 \\
\hline
0 & -2 \\
\hline
1 & -7 \\
\hline
2 & -12 \\
\hline
\end{array}
\][/tex]
From the provided answer, we have the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex]:
- [tex]\( m = -5 \)[/tex]
- [tex]\( b = -2 \)[/tex]
This gives us the linear equation:
[tex]\[
y = -5x - 2
\][/tex]
Let's verify this equation with a few data points:
1. For [tex]\( x = -3 \)[/tex]:
[tex]\[
y = -5(-3) - 2 = 15 - 2 = 13
\][/tex]
Data point: [tex]\( (-3, 13) \)[/tex]
2. For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = -5(-2) - 2 = 10 - 2 = 8
\][/tex]
Data point: [tex]\( (-2, 8) \)[/tex]
3. For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = -5(-1) - 2 = 5 - 2 = 3
\][/tex]
Data point: [tex]\( (-1, 3) \)[/tex]
4. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -5(0) - 2 = -2
\][/tex]
Data point: [tex]\( (0, -2) \)[/tex]
5. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = -5(1) - 2 = -5 - 2 = -7
\][/tex]
Data point: [tex]\( (1, -7) \)[/tex]
6. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = -5(2) - 2 = -10 - 2 = -12
\][/tex]
Data point: [tex]\( (2, -12) \)[/tex]
Thus, the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is correctly given by:
[tex]\[
y = -5x - 2
\][/tex]
