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Co-ordinate ......(alwz stumped)

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by fightthegmat » Sat Sep 05, 2009 4:56 am
In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0, has slope 32. What is the value of b?
(1) a = 4
(2) c = −6

How do i even approach these problems.I get really stumped when it comes to co-ordinate geometry.
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Source: — Data Sufficiency |
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by Nermal » Sat Sep 05, 2009 5:37 am
First we have to bring this equation into a "normal linear equation" in the form: y=mx+n

m is the slope, n is the y-intercept.

This is the first step I would always do when looking at a coordinate geometry problem.

ax+by+c=0

we now "translate" it into the normal linear equation:

y=(-ax-c)/b or y=(-a/b)*x-(c/b)

this gives us the slope of (-a/b) which we know from the question stem equals to 32.

We are supposed to find b.

Statement 1: a=4 ---> b=-8 SUFFICIENT

Statement 2: I cannot read it properly.
But if it only gives a certain value of c this statement is NOT SUFFICIENT since you have 3 unknowns and only two equations.

Therefore I'd say the answer is A.
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