To find a good approximation for the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex], we will use the equation of the line of best fit given by:
[tex]\[ f(x) = -0.86x + 13.5 \][/tex]
We need to substitute [tex]\( x = 18 \)[/tex] into this equation and solve for [tex]\( f(18) \)[/tex].
Step-by-step solution:
1. Start with the equation of the line of best fit:
[tex]\[ f(x) = -0.86x + 13.5 \][/tex]
2. Substitute [tex]\( x = 18 \)[/tex] into the equation:
[tex]\[ f(18) = -0.86(18) + 13.5 \][/tex]
3. Perform the multiplication:
[tex]\[ -0.86 \times 18 = -15.48 \][/tex]
4. Add [tex]\( 13.5 \)[/tex] to the result:
[tex]\[ f(18) = -15.48 + 13.5 = -1.98 \][/tex]
Thus, the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex] is approximately [tex]\( -1.98 \)[/tex].
Among the given choices:
- [tex]\( -5 \)[/tex]
- [tex]\( -2 \)[/tex]
- [tex]\( 3 \)[/tex]
- [tex]\( 12 \)[/tex]
The closest approximation to [tex]\( -1.98 \)[/tex] is [tex]\( -2 \)[/tex].
Therefore, a good approximation for the value of the function when [tex]\( x = 18 \)[/tex] is [tex]\( -2 \)[/tex].
