Question

the equation for the line of best fit is f(x) = 1.8x - 5.4 for the set of values in the table. using the equation for the line of best fit, what is a good approximation for x when f(x) = 30? x f(x) 4 5 5 2 6 5 6 6 8 8 9 7 10 18 14 20 45 54

Explanation:

Step1: Substitute f(x) value

Set \(f(x)=30\) in the equation \(f(x) = 1.8x-5.4\), getting \(30 = 1.8x-5.4\).

Step2: Isolate the term with x

Add 5.4 to both sides of the equation: \(30 + 5.4=1.8x-5.4 + 5.4\), so \(35.4 = 1.8x\).

Step3: Solve for x

Divide both sides by 1.8: \(x=\frac{35.4}{1.8}\approx19.67\approx20\).

Answer:

20