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]
