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Home Q & A Board Science-Related Homework Help Mathematics
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ijustdontknow ijustdontknow
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10 years ago
Not sure if I worded that correctly but anyways.
The problem is:
Find the equation of the line perpendicular to 4x + 3y = 12 that passes through (2, -3)
Please include the steps required to get there and the solution.

Thanks very much!
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#1
10 years ago
first, lets put it in the form of y=mx+b
3y=-4x+12
y=-4/3x+4

Since its perpendicular and passes through the points (2,-3) we know that that the slope of a perpendicular line is the opposite reciprocal of the original given slope, so -4/3 becomes 3/4.

Now, we have y=3/4x+b
So, we plug in the coordinates(2,-3) in for x and y, this will allow us to solve for b.
y=mx+b
-3=3/4(2)+b
-3=6/4+b
-3=3/2+b
-3-3/2=b
-9/2=b

so now we have everything we need, we have the original equation, y=mx+b
we have the slope, 3/4, and b, which is -9/2

y=3/4x-9/2 is the answer

***note*** you may have to rearrange the equation depending on which form your teacher wants, this is in slope intercept form.
wrote...
#2
10 years ago
Perpendicular equations have the slopes, in which the product is -1.

Solve for y for the given equation:

3y = -4x + 12
y = (-4x/3) + 12/3
y = (-4x/3) + 4

By y = mx + b, the slope of the given equation is -4/3.  You can also tell that the slope of another equation is 3/4 since the slopes' product is -1: (-4/3)(3/4) = -1.

By y - y1 = m(x - x1), substitute (2,-3) for (x1,y1) and 3/4 for m:

y - (-3) = 3/4(x - 2)
y + 3 = (3x/4) - (3/4)(2)
y + 3 = (3x/4) - (3/2)
y = (3x/4) - (3/2) - 3
y = (3x/4) - (3/2) - (6/2)
y = (3x/4) - (9/2)

I hope this helps!
wrote...
#3
10 years ago
4x + 3y = 12; solve for y

3y = -4x + 12; divide each term by 3

y  = -4x/3 + 12/3; simplify

y = -4x/3 + 4

The second equation will have the negative reciprocal of -4/3 which is 3/4

Using this and the point (2,-3) you can find the second equation

y = 3/4x + b; substitute in for x and y and solve for b

-3 = 3/4(2) + b
-3 = 6/4 + b; reduce the fraction
-3 = 3/2 + b; subtract 3/2 from each side
-3 - 3/2 = b; get a common denominator between -3/1  and -3/2 which is 2
[-3/1(2/2)] - 3/2 = b ; simplify
-6/2 - 3/2 = b; rewrite
-6-3/2 = b; subtract
-9/2 = b

Now put this all together

y = 3/4x - 9/2 Leftwards Arrow------Answer

Blessings
Answer accepted by topic starter
312312
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#4
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10 years ago
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