anonymous
  • anonymous
If you are finding the line perpendicular to x + 3y = 5, what is the slope of the line? Answer -3/5 1/3 3 -3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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whpalmer4
  • whpalmer4
Solve your equation for \(y\) to get it in slope-intercept form: \(y = mx+b\) where \(m\) is slope. Now divide -1 by \(m\) to get the slope of the perpendicular line. The product of the slopes of perpendicular lines should equal -1 (unless one of them is vertical)
anonymous
  • anonymous
How would you divide m?
whpalmer4
  • whpalmer4
\(m\) is going to be a number. I'll walk you through it. Solve the equation for \(y\): what do you get?

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More answers

anonymous
  • anonymous
What is y again is the answer -1
whpalmer4
  • whpalmer4
Come on, you have the equation \[x +3y = 5\] Solve that for \(y\). In other words, arrange it so \(y = \)
whpalmer4
  • whpalmer4
Do you know how to do that?
whpalmer4
  • whpalmer4
\[x+3y=5\]Subtract \(x\) from both sides: \[x-x+3y = 5-x\]\[3y=5-x\]Divide both sides by 3: \[\frac{3y}{3} = \frac{5-x}{3}\]\[y=-\frac{1}{3}x+\frac{5}{3}\]
whpalmer4
  • whpalmer4
Now, compare that with slope intercept form: \[y=mx+b\] Matching up the respective pieces, what is the value of \(m\)?
anonymous
  • anonymous
ok would you add 1/3x + 5/3 to get m?
whpalmer4
  • whpalmer4
\[y = mx + b\] \[y = -\frac{1}{3}x + \frac{5}{3}\] Match up the pieces! \(y\) matches \(y\). what matches with \(mx\)?
anonymous
  • anonymous
-1/3
whpalmer4
  • whpalmer4
Yes, \[m = -\frac{1}{3}\] Okay, the slope of the other line is \[\frac{1}{m} = \frac{1}{-\frac{1}{3}}=\] Do you know how to divide fractions?
anonymous
  • anonymous
do you flip the fraction and multiply it?
whpalmer4
  • whpalmer4
Flip the fraction in the denominator and multiply by it, yes.
anonymous
  • anonymous
so that would be 1/m times -1/3/1
anonymous
  • anonymous
-1/3/m
whpalmer4
  • whpalmer4
no. we are trying to divide 1 by -1/3. 1 = 1/1 invert -1/3 -> -3/1 1/1 * -3/1 = -3
whpalmer4
  • whpalmer4
Ah, @#$#$, we wanted to divide -1 by m, not 1. Sigh. \[\frac{-1}{m} = \frac{-1}{-\frac{1}{3}}\]to do that, we multiply the numerator (-1) by the inverted denominator (-3/1) \[-1*\frac{-3}{1} = 3\]
anonymous
  • anonymous
okay that makes sense I did not know that
whpalmer4
  • whpalmer4
We need the two slopes to multiply together and give -1 as the answer. Let's see if they do: \[-\frac{1}{3}*3=-\frac{3}{3} = -1\]They do, so 3 is the correct answer for the slope of the perpendicular line.
whpalmer4
  • whpalmer4
Sorry for the confusion due to the missing - sign! This is an example of why I always check my work — I catch silly mistakes like this!
anonymous
  • anonymous
okay great tip " to always check your work" Thank you so much for the help
whpalmer4
  • whpalmer4
Hope it helped!
Jhannybean
  • Jhannybean
Another thing - slope of a perpendicular line follows the format \[m= -\frac{1}{m}\] where -1/m is the slope of the perpendicular line and m is the slope of the line given/found.
dan815
  • dan815
|dw:1371111663753:dw|
dan815
  • dan815
|dw:1371111730143:dw|
dan815
  • dan815
so if u compute the slope of these 2 lines now, with the new coordinates you can see that it will the negative reciprocal of each other
dan815
  • dan815
lemme show u with numbers if those arbritrary variables confuses u
dan815
  • dan815
|dw:1371112077955:dw|
dan815
  • dan815
|dw:1371113527373:dw|
dan815
  • dan815
or i shud say width and height maybe
dan815
  • dan815
|dw:1371113670256:dw|

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