Lord2clash
  • Lord2clash
What is the equation of a line that is perpendicular to and passes through the point (8, 3)?
Mathematics
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Lord2clash
  • Lord2clash
@TheSmartOne could i get help with this?
steve816
  • steve816
perpendicular to what?
Michele_Laino
  • Michele_Laino
please you have to provide the line of reference

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More answers

steve816
  • steve816
Exactly
Lord2clash
  • Lord2clash
sorry didn't realize it wasn't there. its y=4x+5
ShadowLegendX
  • ShadowLegendX
Good ole algebra, miss those days
Michele_Laino
  • Michele_Laino
hint: if I call with \(m\) the slope of the refernce line, and with \(m'\) the slope to the perpendicular line to such reference line, then the subsequent condition holds: \(m \cdot m'=-1\)
Michele_Laino
  • Michele_Laino
reference*
Michele_Laino
  • Michele_Laino
now, I ask what is the slope \(m\) of the line of reference, please?
Lord2clash
  • Lord2clash
-1 since they are perpendicular they have the same slope
Michele_Laino
  • Michele_Laino
hint: what is the slope of this line: \(y=4x+5\) ?
Lord2clash
  • Lord2clash
4 (sorry i got confused xD)
Michele_Laino
  • Michele_Laino
that's right! :) from my formula above we get: \[m' = - \frac{1}{m} = ...?\] please replace \(m=4\), and compute the value of \(m'\). What do you get?
Lord2clash
  • Lord2clash
1/4 = 0.25
Michele_Laino
  • Michele_Laino
more precisely it is \(-1/4\), am I right?
Lord2clash
  • Lord2clash
yes
Michele_Laino
  • Michele_Laino
ok! Now in order to write the requested equation, we can apply this formula: \[y - y_0 = - \frac{1}{4}\left( {x - x_0} \right)\] where \(x_0=8,\;y_0=3\), please replace such values into such equation. What do you get?
Lord2clash
  • Lord2clash
y-3=-1/4 (x-8)
Michele_Laino
  • Michele_Laino
that's right! Now we have to simplify such equation, in order to get an equation of this type: \(y=mx+q\) so, I apply the distributive property of multiplication over addition to the right side, and I get: \[y - 3 = - \frac{x}{4} + 2\] now, please continue
Lord2clash
  • Lord2clash
I don't know what to do from here...
Michele_Laino
  • Michele_Laino
If I add \(3\) to both side, I can write this: \[y - 3 + 3 = - \frac{x}{4} + 2 + 3\] please simplify
Michele_Laino
  • Michele_Laino
sides*
Michele_Laino
  • Michele_Laino
hint: what is \(-3+3=...?\)
ShadowLegendX
  • ShadowLegendX
@Michele_Laino Youʻre a really good helper ^-^
Michele_Laino
  • Michele_Laino
thanks!! :) :) @ShadowLegendX

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