Q26. - 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.

Find an equation of the line through $(x_1,y_1) and (x_3,y_3)$.

Step-by-Step Solution

Answer

The equation of line is $y=21.4x-42,296.2$.

Step-1 – Determine the points.

We know that $x_1=1988,y_1=247,x_3=1998 and y_3=461$

Thus, the coordinates are $(x_1,y_1)=(1988,247) and (x_2,y_2)=(1998,461)$

Step-2 – Calculate the slope.

Substitute $(x_1,y_1)=(1988,247) and (x_2,y_2)=(1998,461)$ into the formula $slope=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}m=\frac{461-247}{1998-1988}\\ m=\frac{214}{10}\\ m=21.4\end{array}$

Step-3 – Make the equation.

Substitute $(x_1,y_1)=(1988,247)$ into $y-y_1=m(x-x_1)$.

 $\begin{array}{l}y-247=21.4(x-1988)\\ y-247=21.4x-42,543.2\\ y=21.4x-42,296.2\end{array}$

The equation of line is $y=21.4x-42,296.2$.