To find a good approximation for [tex]\( x \)[/tex] when [tex]\( f(x) = 30 \)[/tex] using the line of best fit equation [tex]\( f(x) \approx 1.8x - 5.4 \)[/tex]:
Given:
[tex]\[ f(x) = 30 \][/tex]
The equation of the line of best fit is:
[tex]\[ f(x) \approx 1.8x - 5.4 \][/tex]
We need to solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ 30 = 1.8x - 5.4 \][/tex]
Let's solve this step-by-step:
1. First, isolate the term containing [tex]\( x \)[/tex]:
[tex]\[ 30 + 5.4 = 1.8x \][/tex]
[tex]\[ 35.4 = 1.8x \][/tex]
2. Next, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by the coefficient of [tex]\( x \)[/tex], which is 1.8:
[tex]\[ x = \frac{35.4}{1.8} \][/tex]
3. Performing the division:
[tex]\[ x \approx 19.666666666666664 \][/tex]
Given the possible answer choices:
- 14
- 20
- 45
- 54
The closest value to our calculated [tex]\( x \)[/tex] is 20.
Thus, a good approximation for [tex]\( x \)[/tex] when [tex]\( f(x) = 30 \)[/tex] is [tex]\(\boxed{20}\)[/tex].
