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In the diagram, $D$ and $E$ are the midpoints of $\overline{AB}$ and $\overline{BC}$ respectively. Find the sum of the slope and $y$-intercept of the line passing through the points $C$ and $D.$

https://latex.artofproblemsolving.com/5/5/0/55002ffdc5d288b4984c4eba461a467dcced7760.png

Dec 3, 2017

#1
+98196
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Since D is the midpoint of AB   it is  the point  ( 0, 3)  ⇒  y intercept  = 3

And  the points (0,3)  and (8,0)  are on the line through CD

So.....its slope is   [ 3 - 0 ] / [ 0 - 8 ] =  -3/8

So.....the sum of the slope and y intercept of this line  =

-3/8 + 3  =

[-3 + 24 ] / 8  =

21 / 8

Dec 3, 2017