Question

the median home value in north dakota and nevada (adjusted for inflation) are shown below:

year	north dakota	nevada
2000	74400	142000

if we assume that the house values are changing linearly,
a) in which state have home values increased at a higher rate?
b) if these trends were to continue, what would be the median home value in north dakota in 2010?
c) if we assume the linear trend existed before 1950 and continues after 2000, the two states median house values will be (or were) equal in what year? (the answer might be absurd)

Explanation:

Step1: Find the linear - equation formula for North Dakota

The linear - equation formula is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For North Dakota, let $x$ be the number of years since 1950. When $x = 0$ (1950), $y_1=32700$, and when $x = 50$ (2000), $y_2 = 74400$.
The slope $m_1=\frac{y_2 - y_1}{x_2 - x_1}=\frac{74400 - 32700}{2000 - 1950}=\frac{41700}{50}=834$.
Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(0,32700)$, the equation for North Dakota is $y_1=834x + 32700$.

Step2: Find the linear - equation formula for Nevada

When $x = 0$ (1950), $y_3 = 53700$, and when $x = 50$ (2000), $y_4=142000$.
The slope $m_2=\frac{y_4 - y_3}{x_4 - x_3}=\frac{142000 - 53700}{2000 - 1950}=\frac{88300}{50}=1766$.
Using the point - slope form $y - y_3=m(x - x_3)$ with the point $(0,53700)$, the equation for Nevada is $y_2=1766x + 53700$.

Step3: Set the two equations equal to each other to find the year of equal values

Set $y_1=y_2$, so $834x + 32700=1766x + 53700$.
Subtract $834x$ from both sides: $32700 = 1766x-834x + 53700$.
$32700=932x + 53700$.
Subtract 53700 from both sides: $932x=32700 - 53700=-21000$.
$x=\frac{-21000}{932}\approx - 22.53$.
The year is $1950+x=1950-22.53\approx1927.47$.

Answer:

1927