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Question 165220: Find the equation of the line perpendicular to 3x – 4y = 9 and passing through (-2, -1). Write the equation in standard form, with all integer coefficients
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! first, of all we know that lines that are perpendicular have slopes that are negative inverses of each other. The first thing we need to do is to write this in y=mx+b format where m is the slope and b is the y intercept. so we add 4y and subtract -9 from each side then we divide both sides by 4 which gives us
y=3/4x-9/4. so since this equation has a slope of 3/4 we know that any line perpendicular this this line will have a slope of its negative inverse, which is -4/3. Using the formula y-k=m(x-h) where (h,k) is any point on the line. we plug in -4/3 for the slope(m) and the point (-2,-1) for (h,k)....we arrive at
y-(-1)=-4/3(x-(-2)) which simplifies to y+1=-4/3(x+2) multiplying out the right side we get y+1=-4/3x-8/3...subt 1 from each side and we get
y=-4/3x-11/3 to write this with integer coeficients multply both sides by 3 and you get 3y=-4x-ll or 4x+3y+11=0
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