To determine which equation represents the line that fits the given data points, we need to find the slope (m) and the y-intercept (b) of the line. These values will allow us to compose the linear equation in the form [tex]\( y = mx + b \)[/tex].
Given data points:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 16 \\
\hline
-1 & 11 \\
\hline
0 & 6 \\
\hline
1 & 1 \\
\hline
2 & -4 \\
\hline
\end{array}
\][/tex]
We can calculate the slope [tex]\( m \)[/tex] and intercept [tex]\( b \)[/tex], and then compare the resulting linear equation against the provided options:
1. Option A: [tex]\( y = -5x + 3 \)[/tex]
2. Option B: [tex]\( y = -5x + 6 \)[/tex]
3. Option C: [tex]\( y = -3x - 5 \)[/tex]
4. Option D: [tex]\( y = -5x + 9 \)[/tex]
Upon detailed calculation and comparison, we find that:
- The slope [tex]\( m \)[/tex] is [tex]\(-5\)[/tex]
- The intercept [tex]\( b \)[/tex] is [tex]\( 6 \)[/tex]
Hence, the equation that fits the data from the table is:
[tex]\[ \boxed{y = -5x + 6} \][/tex]
This aligns with Option B. Therefore, the correct option is B.
