To find a good approximation for the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex], we use the given equation for the line of best fit:
[tex]\[ f(x) \approx -0.86x + 13.5 \][/tex]
We need to substitute [tex]\( x = 18 \)[/tex] into this equation.
[tex]\[ f(18) \approx -0.86 \cdot 18 + 13.5 \][/tex]
Now, let's follow these steps to find the value:
1. First, compute [tex]\( -0.86 \cdot 18 \)[/tex]:
[tex]\[ -0.86 \cdot 18 = -15.48 \][/tex]
2. Next, add this result to 13.5:
[tex]\[ f(18) \approx -15.48 + 13.5 \][/tex]
3. Perform the addition:
[tex]\[ f(18) \approx -1.98 \][/tex]
Therefore, the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex] is approximately -1.98.
Given the options:
- [tex]$-5$[/tex]
- [tex]$-2$[/tex]
- 3
- 12
The closest value to the calculated result of -1.98 is [tex]\(-2\)[/tex].
Hence, a good approximation for the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex] is [tex]\(-2\)[/tex].
