Solve y = -1/4x - 12 Perpendicular Through (3, -4)

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Discussion Overview

The discussion revolves around finding the equation of a line that is perpendicular to the line given by y = -1/4x - 12 and passes through the point (3, -4). The focus includes the properties of slopes of perpendicular lines and the method to derive the equation from a point and slope.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • Some participants note that the slope of the first line is -1/4 and suggest that the slope of the perpendicular line will be the opposite reciprocal.
  • There is a discussion about terminology, with some preferring "negative reciprocal" over "opposite reciprocal."
  • Participants mention that if the slope of a line is -1/4, the slope of a line that is perpendicular to it would be 4.
  • One participant states that the product of the slopes of two perpendicular lines equals -1, leading to the equation -1 = m1 * m2.
  • There is a suggestion to use the point-slope form to find the full equation of the perpendicular line using the identified slope and the given point.

Areas of Agreement / Disagreement

Participants generally agree on the concept that the slopes of perpendicular lines are related through the product equaling -1, but there is some variation in terminology regarding the slopes. The discussion remains focused on deriving the equation without reaching a final consensus on the complete solution.

Contextual Notes

Some participants reference different terminologies for slopes and the method of finding the equation, which may depend on individual teaching styles or preferences. There is no resolution on the final equation as the discussion is ongoing.

Who May Find This Useful

This discussion may be useful for students learning about the properties of slopes in geometry, particularly in the context of perpendicular lines and line equations.

Poweranimals
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Perpendicular to y = -1/4x - 12 passing through (3, -4).
 
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Hint: If two lines are perpendicular, what does this tell you about their slopes?
 
They intersect?
 
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.
 
opposite reciprocal?

:P

I prefer to use the term negative reciprocal.
 
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!
 
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.
 
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...
 
  • #10
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.
 

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