Answered

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Using the equation for the line of best fit, [tex]f(x) \approx -0.86x + 13.5[/tex], what is a good approximation for the value of the function [tex]f(x)[/tex] when [tex]x = 18[/tex]?

A. -5
B. -2
C. 3
D. 12

Sagot :

GinnyAnswer
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].
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