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If we go state by state and compare the Republican candidate’s 2012 vote share ( $x$ ) to the Republican candidate’s 2016 vote share ( $y$ ), we get the following graph where a trendline has been superimposed.

Find a point-slope equation for this line. (Note that a slope-intercept equation would use the $y$ -intercept coordinate $b\text{,}$ and that would not be meaningful in context, since no state had anywhere near zero percent Republican vote.)

Solution

We need to calculate slope first. And for that, we need to identify two points on the line. Conveniently, the line appears to pass right through $(50,50)\text{.}$ We have to take a second point somewhere, and $(75,72)$ seems like a reasonable roughly accurate choice. The slope equation gives us that

$m=\frac{72-50}{75-50}=\frac{22}{25}=0.88\text{.}$

Using $(50,50)$ as the point, the point-slope equation would then be

$y=0.88(x-50)+50\text{.}$