Question 953387
First find the point of intersection.
The line going through the two points has a slope of 
{{{m=(9-(-1))/(8-3)=10/5=2}}}
So the equation of the line is,
{{{y-9=2(x-8)}}}
{{{y-9=2x-16}}}
{{{y=2x-7}}}
Then,
{{{x-(2x-7)-2=0}}}
{{{x-2x+7-2=0}}}
{{{-x+5=0}}}
{{{x=5}}}
and
{{{y=2(5)-7}}}
{{{y=10-7}}}
{{{y=3}}}
So the intersection point is (5,3).
Now you can use either the x values or y values to calculate the ratio.
X values,
{{{(5-3)/(8-3)=2/5}}}
Y values,
{{{(3-(-1))/(9-(-1))=4/10=2/5}}}
You will get the same answer.
{{{R=2/5}}}
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{{{drawing(300,300,-2,10,-2,10,grid(1),blue(line(3,-1,8,9)),circle(3,-1,0.3),circle(8,9,0.3),circle(5,3,0.3),graph(300,300,-2,10,-2,10,x-2))}}}