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Triangle ABC has vertices A(0, 8), B(2, 0),C(8, 0). A line through B cuts the area of \(\triangle ABC\) in half; find the sum of the slope and y-intercept of this line.

Guest Dec 13, 2018

#1**+1 **

The height of ABC = 8

The midpoint of (2,0) and (8,0) = (5,0)

And the line connnecting (0,8) and (5,0) will divide the area of the orginal triangle in half

The slope of this line is [ 8 - 0 ] / [ 0 - 5 ] = 8 / -5 = -8/5

The equation of this line is

y = - (8/5)x + 8

The y intercept = 8

So....the sum of the slope and y intercept = -8/5 + 8 = 32 / 5

Here's a graph :

CPhill Dec 13, 2018