The end points of line segment ab are a(3, -12) and b(6, k) what is the value of k if the slope of a line segment is -2? show your work.

Two points determine a line.  In slope intercept form we have:
y = -2x + b

So:
-12 = -2(3) + b  and [first equation]
k = -2(6) + b [second equation]

We have a system of simultaneous equations with two unknowns.  The first is trivially easy to solve:

-12 = -6 + b  [Evaluate -2(3)]
-6 = b  [Add +6 to each side]

So we substitute this into the second equation:
k = -2(6) + -6 = -18

We could double check our work knowing that m=Δy/Δx

We expect m to be -2.  Does:
-2 = (-18 - -12)/(6 - 3) = -6/3 = -2?

;)

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