SOLUTION: Perpendicular Lines: Write the equation of the line through (4,5) and perpendicular to the line with equation 3x + 2y = -1. Please explain how the equation came out to y = 2/3 x

Algebra ->  Linear-equations -> SOLUTION: Perpendicular Lines: Write the equation of the line through (4,5) and perpendicular to the line with equation 3x + 2y = -1. Please explain how the equation came out to y = 2/3 x      Log On


   

Question 260757: Perpendicular Lines: Write the equation of the line through (4,5) and perpendicular to the line with equation 3x + 2y = -1.
Please explain how the equation came out to y = 2/3 x + 7 as shown in my example answer key.
Thank you,
Melissa
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, we must solve for y to get the equation in slope intercept form.


3x+%2B+2y+=+-1 Start with the given equation


2y+=+-1-3x Subtract 3x from both sides.


2y+=+-3x-1 Rearrange the terms.


y+=+%28-3x-1%29%2F2 Divide both sides by 2 to isolate y.


y+=+%28-3%2F2%29x-1%2F2 Break up the fraction and simplify.


So the equation y+=+%28-3%2F2%29x-1%2F2 is now in slope intercept form y=mx%2Bb where the slope is m=-3%2F2 and the y intercept is b=-1%2F2

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Recall that perpendicular lines have slopes that are negative reciprocals of one another. So because the slope of the given line is -3%2F2, the perpendicular slope is 2%2F3 (just flip the fraction and change the sign).


So we now know that the slope of the perpendicular line is m=2%2F3 and it goes through the point (4,5).


Now let's use the point-slope formula to find the perpendicular equation.


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point-slope formula


y-y%5B1%5D=%282%2F3%29%28x-x%5B1%5D%29 Plug in m=2%2F3


y-5=%282%2F3%29%28x-4%29 Plug in x%5B1%5D=4 and y%5B1%5D=5. This is given from (4,5). Our goal now is to solve for y.


y-5=%282%2F3%29x-%282%2F3%294 Distribute


y-5=%282%2F3%29x-8%2F3 Multiply


y=%282%2F3%29x-8%2F3%2B5 Add 5 to both sides.


y=%282%2F3%29x%2B7%2F3 Combine like terms.

So the equation of the perpendicular line is y=%282%2F3%29x%2B7%2F3 (make sure that there isn't a typo). Notice that if we graph the two lines, we get



Graph of y=%28-3%2F2%29x-1%2F2 (red) and y=%282%2F3%29x%2B7%2F3 (green) going through the point (4,5). Notice how the red line is perpendicular to the green line.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Glad you provided the answer you have.
First we have to find the slope of the given line
3x+2y=-1
Get y by itself
2y=-3x-1
y=-3x/2-1/2
The slope is -3/2
So the perpendicular line has to have a slope of 2/3
2/3*(-3/2)=-1
The new line goes through (4,5)
Plug in 4 and 5 to find b
5=2*4/3+b
15/3-8/3=b
7/3=b
y=2x/3+7/3
or 3y=2x+7