# A Difficult Equation

## Main Question or Discussion Point

Perpendicular to y = -1/4x - 12 passing through (3, -4).

Math Is Hard
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Hint: If two lines are perpendicular, what does this tell you about their slopes?

They intersect?

Math Is Hard
Staff Emeritus
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well, the lines intersect, yes. but you know what the slope of the first line is, right? your equation is in y =mx+b format so you can tell just by looking.

the slope of the second line will be the opposite reciprocal of the first slope.

NSX
opposite reciprocal?

:P

I prefer to use the term negative reciprocal.

Math Is Hard
Staff Emeritus
Gold Member
I grew fond of "opposite" because there's no confusion if you are talking about the slope of a line that's perp to a line with a negative slope. but that's just me!

Math Is Hard
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anyhoo, power animals, what we're saying is that if a line has a slope of positive 3, for example, then the slope of a line that is perpendicular to it would be -1/3.

Math Is Hard
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so if the slope of a line is -1/4, then the slope of a line that is perpendicular to it would be...?

or when you multiply both slopes together you get -1 ?

my maths teacher had a strange way of explaining things...

yes. when multiplied together they will equal -1

so you can see it by setting -1=m1*m2 where m1 or m2 to -1/4.

do you need help finding the whole equation based on that slope and point? you can just plug an x and a y into the y=mx+b way and solve for b too.