Question

housing the data show the median price of an existing home in the united states from 2011 to 2016.
use the points (1, 226.9) and (4, 275.2) to enter and interpret an equation for the line of fit in slope - intercept form. let x be the number of years since 2010 and y the median price in thousands of dollars.
if the trend continues, what will be the approximate median price of an existing home in 2025? about $

Explanation:

Step1: Calculate the slope ($m$)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given the points $(x_1,y_1)=(1,226.9)$ and $(x_2,y_2)=(4,275.2)$.
$m=\frac{275.2 - 226.9}{4 - 1}=\frac{48.3}{3}=16.1$

Step2: Find the $y$ - intercept ($b$)

Use the point - slope form $y - y_1=m(x - x_1)$ with $m = 16.1$ and $(x_1,y_1)=(1,226.9)$.
$y-226.9=16.1(x - 1)$
$y-226.9=16.1x-16.1$
$y=16.1x+210.8$

Step3: Interpret the slope and $y$ - intercept

The slope $m = 16.1$ means the median price of an existing home increases about $\$16100$ each year (since $x$ is in years and $y$ is in thousands of dollars). The $y$ - intercept $b = 210.8$ means the price of a home was about $\$210800$ in 2010 (when $x = 0$).

Step4: Predict the price in 2025

For 2025, $x=2025 - 2010=15$
Substitute $x = 15$ into $y=16.1x+210.8$
$y=16.1\times15+210.8$
$y = 241.5+210.8$
$y=452.3$ (in thousands of dollars)

Answer:

$y = 16.1x+210.8$; The median price of an existing home increases about $\$16100$ each year. The price of a home was about $\$210800$ in 2010. If the trend continues, the approximate median price of an existing home in 2025 is about $\$452300$.