Answer
a) $y = -720x + 271,500$
b)$265,740$ dollars
Work Step by Step
a) So let's start with the simple equation $y = mx + b$. The question gives us the average value of a house in 2004, which is when $x = 0$. When $x = 0$,
$y$ is equal to $271,500$. $271,500$ is the $y$-intercept. So far we have this.
$y = mx + 271,500$
We need to find the value of $m$ (The slope). The question gives us two points, $(0, 271500)$ and $(5,267900)$. Using the slope formula, $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$, we get the slope as $-720$
so now we have the equation.
$y = -720x + 271,500$
b) 2012 is $8$ years after 2004. Therefore $x=8$. Plug it in to the equation we have just made.
$y = -720 * 8 + 271,500$
$y = -5760 + 271,500$
$y = 265,740$
