Question #139986
Determine the equation of the line perpendicular to 3y + 4x = 1 and passing through the point A (-1, 4)
1
Expert's answer
2020-10-25T18:35:32-0400

Answer\bold {Answer}


4y3x=194y -3x = 19


Solution\bold {Solution}

The the products of the gradients of perpendicular lines is 1-1 , that is, mm=1mm' = -1 where mm is the gradient of one line and mm' is the gradient of a line perpendicular to the first line.


The general form of a straight line equation is y=mx+cy = mx + c . Reducing 3y+4x=13y +4x = 1 to standard form gives:

3y+4x=13y + 4x = 1

=>3y=4x+1=> 3y = -4x + 1


=>3y3=4x3+13=> \dfrac {3y}{3} = \dfrac {-4x}{3} + \dfrac {1}{3}


=>y=43x+13=> y = -\dfrac {4}{3}x + \dfrac {1}{3}


Now, the gradient is 43-\dfrac {4}{3}


Since mm=1mm' = -1

=>43m=1=> -\dfrac {4}{3}m' = -1

=>4m=1×3=> -4m' = -1 × 3

=>m=34=> m' = \dfrac {-3}{-4}


=34= \dfrac {3}{4}


Thus, the perpendicular line has gradient 34\dfrac {3}{4}


The equation of the perpendicular line through A\bold A is given by:


yy1=m(xx1)y - y_{1} = m'(x-x_{1})

=>y4=34(x(1))=> y - 4 = \dfrac {3}{4} (x - (-1))


=>y=34(x+1)+4=> y = \dfrac {3}{4}(x+1)+4


=>4y=3(x+1)+16=>4y = 3(x+1) + 16


=>4y=3x+3+16=> 4y = 3x + 3+16


=>4y3x=19=> 4y -3x = 19


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS