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?
14
20
45
54

Explanation:

Step1: Sustituir \(f(x)\) en la ecuación

Sustituimos \(f(x) = 30\) en \(f(x)=1.8x - 5.4\) para obtener \(30 = 1.8x-5.4\).

Step2: Aislar el término con \(x\)

Sumamos 5.4 a ambos lados: \(30 + 5.4=1.8x\), es decir \(35.4 = 1.8x\).

Step3: Calcular el valor de \(x\)

Dividimos ambos lados por 1.8: \(x=\frac{35.4}{1.8}\approx19.67\), que se aproxima a 20.

Answer:

1. First, substitute \(f(x) = 30\) into the equation \(f(x)=1.8x - 5.4\). We get the equation \(30 = 1.8x-5.4\).
2. Then, add \(5.4\) to both sides of the equation:

• \(30 + 5.4=1.8x-5.4 + 5.4\).
• \(35.4 = 1.8x\).

1. Next, solve for \(x\) by dividing both sides of the equation by \(1.8\):

• \(x=\frac{35.4}{1.8}\approx19.67\approx20\).

So the answer is 20.