Answer
a. $y = 0.2x + 5$.
b. $y = -0.4x + 47$.
c. $2030$, $19\%$
Work Step by Step
a. the slope formula is, $\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = m$.
for $x$ years after $1960$, the year $1960$ will be a year zero.
$x_{1}=0, y_{1}=5$ and $x_{2}=48, y_{2}=14$.
$\frac{14-5}{48-0} = \frac{9}{48} =\frac{3}{16} = m$,
to write it in the slope-intercept form of $y=mx+b$,
$\frac{y -5}{x-0} = \frac{3}{16}$,
$y = \frac{3x}{16} + 5$, expressing the slope as a decimal and rounding the slope to one decimal place,
$y = 0.2x + 5$.
b. $x_{1}=0, y_{1}=47$ and $x_{2}=48, y_{2}=27$.
$\frac{27-47}{48-0} = \frac{-20}{48} =\frac{-5}{12} = m$,
to write it in the slope-intercept form of $y=mx+b$,
$\frac{y -47}{x-0} = \frac{-5}{12}$,
$y = \frac{-5x}{12} + 47$, expressing the slope as a decimal and rounding the slope to one decimal place,
$y = -0.4x + 47$.
c. $ 0.2x + 5= -0.4x + 47$,
$0.6x=42$,
$x=70$
Year $1960+70=2030$.
$y=0.2(70)+5=19$.
The percentage will be $19\%$.
