Q28. - Algebra 2

Question

For exercise 25-30, use the following information.

A median-fit line is a particular type of line of fit. Follow the steps below to find the equation of the median-fit line for the data.

28. The median-fit line is parallel to the line in Exercise 26 but is one-third closer to $(x_2,y_2)$. This means it passes through $\left(x_2,\frac{2}{3}Y+\frac{1}{3}{y}_2\right)$. Find this ordered pair.

Step-by-Step Solution

Answer

The ordered pair is $(1993,356.17)$.

Step-1 – Equation of line.

We know that the medians of x-values $x_1=1988,x_2=1993,x_3=1998$ and medians of y-values is $y_1=247,y_2=360.5,y_3=461$

The value of $Y=354$.

Also, the coordinates are $\left(x_2,\frac{2}{3}Y+\frac{1}{3}{y}_2\right)$.

Step-2 – Substitute the respective values.

Substitute $Y=354, and y_2=360.5$ into $\frac{2}{3}Y+\frac{1}{3}{y}_2$

$\frac{2}{3}Y+\frac{1}{3}{y}_2=\frac{2}{3}\left(354\right)+\frac{1}{3}(360.5)$

Step-3 – Simplify the equation.

$\begin{array}{l}\frac{2}{3}Y+\frac{1}{3}{y}_2=\frac{2}{3}\left(354\right)+\frac{1}{3}\left(360.5\right)\\ \approx 236+120.17\\ =356.17\end{array}$

Since $x_2=1993$ thus, the ordered pair is $(1993,356.17)$.