Q10. - Algebra 2

Question

For Exercises 10-12, use the graph that shows how much Americans spent on doctors’ visits in some recent years.

10. Write prediction equation from the data for 1990, 1995, and 2000.

Step-by-Step Solution

Answer

A prediction equation is $y=35.2x-69,485$

Step-1 – Concept of prediction equation.

Prediction equation – An equation of line of fit is often called a prediction equation.

Step-2 – Calculate slope

Using points $(1990,563) and (1995,739)$

$\begin{array}{l}Slope=\frac{739-563}{1995-1990}[\because \text{ Slope =}\frac{y_2-y_1}{x_2-x_1}]\\ =\frac{176}{5}\\ =35.2\end{array}$

Step-3 – Determine equation of line.

Point slope form:$(y-y_1)=m(x-x_1)$

Substituting the respective values

$\begin{array}{l}(y-563)=35.2(x-1990)\\ y-563=35.2x-70,048\\ y=35.2x-69,485\end{array}$

Hence, a predicted equation is  $y=35.2x-69,485$