LifeIsADangerousGame
  • LifeIsADangerousGame
help with Perpendicular and slope?
Linear Algebra
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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LifeIsADangerousGame
  • LifeIsADangerousGame
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mathstudent55
  • mathstudent55
This is what you need to do: 1. Find the slope of the given line. 2. Find the slope of the perpendicular line. 3. Find the equation of the perpendicular.
LifeIsADangerousGame
  • LifeIsADangerousGame
How do I find the slope when its in Standard form?

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mathstudent55
  • mathstudent55
1. If you rewrite the equation of the given line in the form \( y = mx + b\) then the slope is simply m. All you need to do is solve the equation of the given line for y.
LifeIsADangerousGame
  • LifeIsADangerousGame
I tried that but I got stuck, here's what I had 2x + 4y = 5 ÷4 ÷4 2x + y = 5/4 What do I do now?
mathstudent55
  • mathstudent55
\(2x + 4y = 5\) First, you subtract the 2x term from both sides to move it to the right side. \(4y = -2x + 5\)
mathstudent55
  • mathstudent55
Now you divide both sides by 4 to get y by itself.
LifeIsADangerousGame
  • LifeIsADangerousGame
2x + 4y = 5 -2x -2x 4y = -2x + 5 ÷4 ÷4 y = -2/4x - 5/4 THat right?
LifeIsADangerousGame
  • LifeIsADangerousGame
+ 5/4 not negative
mathstudent55
  • mathstudent55
\(y = −\dfrac{2}{ 4} x+\dfrac{5}{ 4 } \) Which can be reduced to: \(y = −\dfrac{1}{2} x+\dfrac{5}{ 4 } \) Now that we have the equation of the given line in the slope-intercept form, \(y=\color{red}{m}x+b\) , it's easy to see what the slope, m, is: \(y = \color{red}{−\dfrac{1}{2}} x+\dfrac{5}{ 4 } \) m is the slope, so in our case, \(m=−\dfrac{1}{ 2} \).
LifeIsADangerousGame
  • LifeIsADangerousGame
So in order to make the other line perpendicular, the slope has to be 1/2x + 5/4?
mathstudent55
  • mathstudent55
Ok, we have done step 1. We know the slope of the given line is \(-\dfrac{1}{2} \). 2. Now we need to find the slope of the perpendicular line. This is rhe rule you need to memorize: \( \bf\color{red}{The ~slopes ~of ~perpendicular ~lines ~are ~negative ~reciprocals.} \)
mathstudent55
  • mathstudent55
Reciprocals are two number whose product is 1. Negative reciprocals are numbers whose product is -1.
mathstudent55
  • mathstudent55
That may sound complicated, but it is simple. To find the reciprocal of a nunber, all you need to do is write the number as a fraction, and then flip the fraction. To find the negative reciprocal of a number, write the number as a fraction, then flip the fraction, then change the sign.
mathstudent55
  • mathstudent55
We already have the slope of our line writen as a fraction, \( -\dfrac{1}{2} \). To find the negative reciprocal, we flip the fraction and change the sign, so we get: \(\dfrac{2}{1} \) which is simply 2. The slope of the perpendicular is 2.
mathstudent55
  • mathstudent55
That concludes step 2. Now we know the slope of the perpendicular is 2. Now we move on to step 3, finding the equation of the perpendicular line.
mathstudent55
  • mathstudent55
Are you following so far?
LifeIsADangerousGame
  • LifeIsADangerousGame
Yes, it makes sense to me so far thanks ^_^
mathstudent55
  • mathstudent55
Ok, let's do step 3. 3. The equation of a line in the slope-intercept form is y = mx + b We can use the slope we have, m = 2, and we can use the point we were given (-8, 2) in the equation. Then the only unknown will be b, the y-intercept. Let's do that. Substitute -8 for x, 2 for y, and 2 for m. We get this equation: 2 = 2(-8) + b which we can solve easily for b.
mathstudent55
  • mathstudent55
2 = 2(-8) + b 2 = -16 + b Add 16 to both sides: 18 = b
mathstudent55
  • mathstudent55
Now that we know b = 18, we can write the equation of the line in y = mx + b form: y = 2x + 18
mathstudent55
  • mathstudent55
If you need the answer in standard form, then you can write it as: y = 2x + 18 0 = 2x - y + 18 -18 = 2x - y 2x - y = -18
mathstudent55
  • mathstudent55
If the problem had asked for the equation of the line that is PARALLEL to the given line instead of perpendicular, then the only difference is that parallel lines have the same slope. That means, after finding the slope of the given line in step 1, then for step 2, you use the same slope. Then you move on to step 3 to find the equation of the parallel line.
LifeIsADangerousGame
  • LifeIsADangerousGame
Ohh okay, thank you Mathstudent! c: I appreciate it!
mathstudent55
  • mathstudent55
You're welcome.

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