Answer
a) $y-45.2=0.65(x-10)$
b) $y=0.65x+38.7$
c) $61.45$%
Work Step by Step
a) To find the slope for the graph, given $(10, 45.2)$ and $(20, 51.7)$. using the formula of slope $$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1})}=\frac{51.7-45.2}{20-10}=6.5/10=0.65.$$ To find the point-slope form use the formula of point slope form $y-y_{1}=m(x-x_{1})$. Inserting the given co-ordinates into the formula will result in $$y-45.2=0.65(x-10).$$
b) To find the slope-intercept form, we can distribute the slope $0.65$ over $(x-10)$ we get $y-45.2=0.65x-6.5$ and then by adding $45.2$ to both sides we get $$y=0.65x+38.7.$$
c) To find the percentage of never-married American males in $2015$, $2015$ will be $35$th years after the year $1980$. Therefore, $x=35$, by inserting it into the formula $$f(x)=0.65(35)+38.7=61.45.$$
