#### Answer

a. $y=-x +52$
b. $y=1.2x +16$
c. $16$ years after 2000 or in year 2016.

#### Work Step by Step

a. Based on the given graph, with $x=year-2000$, we can identify two points on the soda line as $(0,52)$ and $(15,37)$. We can find the slope as $m=\frac{37-52}{15-0}=\frac{-15}{15}=-1$. We can write the line equation as $y-52=-(x-0)$ or in slope-intercept form as $y=-x +52$
b. Based on the given graph, with $x=year-2000$, we can identify two points on the bottled water line as $(0,16)$ and $(15,34)$. We can find the slope as $m=\frac{34-16}{15-0}=\frac{18}{15}=1.2$. We can write the line equation as $y-16=1.2(x-0)$ or in slope-intercept form as $y=1.2x +16$
c. Let $-x +52=1.2x +16$; we have $2.2x=36$ and $x\approx16$ years after 2000 or in year 2016.