SOLUTION: Find the distance from the point (6,1) to the graph of 2x-3y+7=0

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Question 941300: Find the distance from the point (6,1) to the graph of 2x-3y+7=0
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
-3y=-2x-7
y=%282%2F3%29x%2B7%2F3

What is the line perpendicular to that one (given) and containing point (6,1)?
Slope will be -3%2F2. Using point-slope form to find the line,
y-1=-%283%2F2%29%28x-6%29
y-1=-3x%2F2%2B9
y=-%283%2F2%29x%2B10


What is the intersection point of the two line?
%282%2F3%29x%2B7%2F3=-%283%2F2%29x%2B10
%282%2F3%2B3%2F2%29x%2B7%2F3=10
%284%2B9%29x=10%2A6-%287%2F3%29%2A6
13x=60-14
13x=46
highlight_green%28x=46%2F13%29
y=-%283%2F2%29%2846%2F13%29%2B10
y=-138%2F26-15
y=%28-138-90%29%2F26
highlight_green%28y=8%2610%2F13%29

Finally, use the distance formula to find how far are the two points ( 46/13, 8&10/13) from (6,1).