Answer
a. $y = -1.6x + 65$,
b. $y = 1.5x + 30$,
c. $2010$, $y=46.935$ or $47\%$
Work Step by Step
a. The slope formula is,
$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = m$.
for $x$ years after $1999$, the year $1999$ will be a year zero.
$x_{1}=0, y_{1}=65$ and $x_{2}=10, y_{2}=49$.
$\frac{49-65}{10-0} = \frac{-16}{10} =-1.6 = m$,
to write it in the slope-intercept form of $y=mx+b$,
$\frac{y-65}{x-0} = -1.6$,
$y = -1.6x + 65$,
b.$x_{1}=0, y_{1}=30$ and $x_{2}=10, y_{2}=45$.
$\frac{45-30}{10-0} = \frac{15}{10} =1.5 = m$,
to write it in the slope-intercept form of $y=mx+b$,
$\frac{y -30}{x-0} = 1.5$,
$y = 1.5x + 30$,
c. $ -1.6x + 65= 1.5x + 30$,
$35=3.1x$,
$x=11.3$ or $x=11^{th} year$.
Year: $1999+11=2010$
when $y=46.935$ or $47\%$
