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Create a linear model for the data in the table.

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 5 & 7 & 9 & 11 \\
\hline
$y$ & 6 & 16 & 20 & 15 \\
\hline
\end{tabular}
\][/tex]

Write a linear model for the data in the form [tex]\( y = mx + b \)[/tex].

[tex]\( y = \_\_\_ x + \_\_\_ \)[/tex]

(Type integers or decimals rounded to three decimal places as needed.)

Sagot :

GinnyAnswer
To create a linear model [tex]\( y = mx + c \)[/tex] for the data given in the table, we need to determine the slope [tex]\( m \)[/tex] and the intercept [tex]\( c \)[/tex] of the best-fit line.

The data points provided are:
- [tex]\((5, 6)\)[/tex]
- [tex]\((7, 16)\)[/tex]
- [tex]\((9, 20)\)[/tex]
- [tex]\((11, 15)\)[/tex]

Based on the given data, the calculated values for the slope [tex]\( m \)[/tex] and the intercept [tex]\( c \)[/tex] of the linear model are:
- Slope ([tex]\( m \)[/tex]): 1.550
- Intercept ([tex]\( c \)[/tex]): 1.850

Therefore, we can write the linear model for the data as:
[tex]\[ y = 1.550x + 1.850 \][/tex]

So the final linear model is:
[tex]\[ y = \boxed{1.550}x + \boxed{1.850} \][/tex]
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