SOLUTION: (reasoning) consider the equation Ax+By=C a. what must be true of the equation if its graph is a vertical line? b. what must be true of the equation if its graph is a horizontal

Algebra ->  Linear-equations -> SOLUTION: (reasoning) consider the equation Ax+By=C a. what must be true of the equation if its graph is a vertical line? b. what must be true of the equation if its graph is a horizontal       Log On


   

Question 960152: (reasoning) consider the equation Ax+By=C
a. what must be true of the equation if its graph is a vertical line?
b. what must be true of the equation if its graph is a horizontal line?
please help me! i have no clue what they want me to do. i don't know where to start. this problem makes absolutely no sense to me. Can you help me understand? (step by step)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When they say " the graph is a vertical line" that
is the same as saying the slope is infinite
Slope = [ change in y ] / change in x ]
If there is zero change in +x+, then
slope = [ delta y ] / 0
slope = infinity
The equation becomes +x+=+k+ because
+y+ can be anything, but +x+ is whatever
value you pick for it ( whatever +k+ )
Suppose I say +x+=+7+ then
+y+=+-%28A%2FB%29%2Ax+%2B+C+
+y+=+-%28A%2FB%29%2A7+%2B+C+
+B+ approaches zero, so
+y+ cannot be determined
Note that this vertical line is NOT a function.
A function must have a unique +y+ for
any +x+ that you choose.
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A horizontal line means slope = +0+
+y+=+-%28A%2FB%29%2Ax+%2B+C+
+-%28A%2FB%29+=+0+
so, +y+=+C+
is the equation
You can't pick any +y+, the equation already says
+y+=+C+
This line is a function, since any +x+ chosen
gives me a unique +y+ ( It's always the same +y+,
but I don't get MORE than one +y+
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Hope this helps
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