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.
+128474 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 :
