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

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) (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 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 where m is the slope and b is the y-intercept when x=0 or at point(0,b).

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

Divide 2 to both sides of the equation

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 since . Then the equation so far is . 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

Multiply by 3 to both sides of the equation to get

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

Divide 3 to both sides of the equation

Step 4. The equation of the perpendicular line is

A graph of the two lines are described below:

The red line is or and the green line is 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) (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 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions 3x/2 -3 and -2x/3 +20/3).
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