Answer: b = -2
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Work Shown:
m = (y2-y1)/(x2-x1)
m = (b-4)/(6-(-2))
m = (b-4)/(6+2)
m = (b-4)/8
Set this equal to the slope -3/4 and solve for b
(b-4)/8 = -3/4
4*(b-4) = 8*(-3) ... cross multiply
4b-16 = -24
4b = -24+16 ... adding 16 to both sides
4b = -8
b = -8/4
b = -2
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Since b = -2, we can replace b with -2
That makes the point (6,b) turn into (6,-2)
Now apply the slope formula to (-2,4) and (6,-2). We should get -3/4 as a result
m = (y2-y1)/(x2-x1)
m = (-2-4)/(6-(-2))
m = (-2-4)/(6+2)
m = -6/8
m = -3/4
So everything works out.
