Question: px+qy+r

Comment on px+qy+r

brownpure - October 17, 2018
Hi Brent, for line questions such as these ones, I just wanted to ask for a tip.

Is it safe to assume that the following equation: px+qy+r=0 implies that if it re-arranged as a slope/equation of a formula, it becomes :

px+qy+r=0 --> as an equation of a line --> y= -px/q +r/q

So my question is, will the GMAT test-makers ever try to throw in a trick where "x" in the given equation is actually y value and/or the "y" is actually the "x" value?

Implying that the equation would then become:

px+qy+r=0 --> as an equation of a line --> x= -qy/p + r/p

Thanks!
gmat-admin's picture

gmat-admin - October 18, 2018

Almost!

If a line is defined as px + qy + r = 0, then we can write: y = -px/q - r/q (you have + r/q)

Here, the slope = -p/q and the y-intercept = -r/q

To answer your other question, I've never seen an official GMAT question in which the x-axis and the y-axis are switched. In fact, the term "x-y coordinate plane" assumes that the x-axis is the horizontal axis, and the y-axis the vertical one.

Cheers,
Brent

Kimberly750 - November 4, 2022
Hi Brent, if I got y = -r/q - px/q. So y-intercept is -r/q here. Then both St1 and St2 will be positive 3/2. Would that still be correct? Thanks Brent
gmat-admin's picture

gmat-admin - November 4, 2022

That's correct.

Kimberly750 - November 4, 2022
Great to know and thanks Brent for confirmation.
However positive slope and negative slope from this will mean the same in other areas of calculations as well ? or if any difference where will that be? Thanks Brent
gmat-admin's picture

gmat-admin - November 4, 2022

Keep in mind that, from the given equation, we know that the line's slope = -p/q, and the y-intercept = -r/q.
However, we can't conclude that, since the slope is equal to -p/q, the slope must be negative.
Just because it features a negative symbol, doesn't mean the value of -p/q is negative.
For example, if p = 6 and q = -2, then -p/q = -(6)/(-2) = 3

Kimberly750 - November 4, 2022
Great explanation and thanks Brent. -p/q doesn't mean slope is negative or positive but only final result of calculations with numbers will dictate slope is negative or positive.Thanks Brent

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