Answer
a) $y-31.1=0.78(x-10)$
b) $y=0.78x+23.3$
c) $54.5$%
Work Step by Step
a) To find the slope for the graph, given $(10, 31.1)$ and $(20, 38.9)$. using the formula of slope $$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{38.9-31.1}{20-10}=7.8/10=0.78.$$
To find the point-slope form use the formula of point slope form $$y-y_{1}=m(x-x_{1})$$ Insert the given co-ordinates into the formula, we will obtain $$y-31.1=0.78(x-10).$$
b) To find the slope-intercept form, we can distribute the slope $0.78$ over $(x-10)$ we get $$y-31.1=0.78x-7.8$$ and then by adding $31.1$ to both sides we get $$y=0.78x+23.3$$
c) To find the percentage of never-married American females in $2020$, $2020$ will be $40$th years after the year $1980$. Therefore, $x=40$, by inserting it into the formula $y=0.78(40)+23.3=54.5$.
