SOLUTION: Find An Equation Of The Line Perpendicular To 3x-2y = 6, And Passing Through The Point (7,2)?

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Question 214487: Find An Equation Of The Line Perpendicular To 3x-2y = 6, And Passing Through The Point (7,2)?
Found 2 solutions by drj, checkley77:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find An Equation Of The Line Perpendicular To 3x-2y = 6, And Passing Through The Point (7,2)?

Step 1. Need to find slope of 3x-2y=6 so we can determine the slope of the perpendicular line. We also note that two lines are perpendicular when the product of their slopes is equal to -1. To determine the slope, let's put the equation in slope-intercept form given as y=mx%2Bb where m is the slope and b is the y-intercept when x=0 or at point(0,b).

3x-2y=6

Add 2y-6 to both sides of the equation to get

3x-2y%2B2y-6=6%2B2y-6

3x-6=2y

Divide 2 to both sides of the equation

%283x-6%29%2F2=2y%2F2

3x%2F2-3=y

y=3x%2F2-3

Step 2. Based on the last equation the slope m is 3/2 and the y-intercept b=-3.

Step 3. Therefore the slope of the perpendicular line is -2%2F3 since %28-2%2F3%29%283%2F2%29=-1. Then the equation so far is y=-2x%2F3%2Bb. To find b, we know that this line must past through point (7,2) or x=7 and y=2. Substitute these values into the linear equation

y=-2x%2F3%2Bb

2=-2%2A7%2F3%2Bb

Multiply by 3 to both sides of the equation to get

6=-14%2B3b

Add 14 to both sides of the equation to isolate the b-term.

6%2B14=-14%2B3b%2B14

20=3b

Divide 3 to both sides of the equation

20%2F3=3b%2F3

20%2F3=b

b=20%2F3

Step 4. The equation of the perpendicular line is y=-2x%2F3%2B20%2F3

A graph of the two lines are described below:

graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+3x%2F2-3%2C+-2x%2F3%2B20%2F3%29

The red line is 3x-2y+=+6 or y=3x%2F2-3 and the green line is y=-2x%2F3%2B20%2F3 which passes through the point (7,2).

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J




Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
3x-2y = 6, And Passing Through The Point (7,2)?
-2Y=-3X+6
Y=-3X/-2+6/-2
Y=3X/2-3 (RED LINE) WITH A SLOPE=3/2.
A PERPENDICULAR LINE HAS A SLOPE=-2/3
2=-2/3*7+b
2=-14/3+b
b=2+14/3
b=6/3+14/3
b=20/3 the y intercept
Y=-2x/3+20/3 is this perpendicular line equation. (green line).
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2F2+-3%2C+-2x%2F3+%2B20%2F3%29+ (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions 3x/2 -3 and -2x/3 +20/3).