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Sagot :
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.
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.
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