The equation of line perpendicular to given line passing through (8,-5) is:
![y = -\frac{3}{4}x +1](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B4%7Dx%20%2B1)
Step-by-step explanation:
Given equation of line is:
![4x-3y = 15\\3y = 4x -15\\\frac{3y}{3} = \frac{4x-15}[3}\\y = \frac{4}{3}x - \frac{15}{3}\\ y = \frac{4}{3}x - 5](https://tex.z-dn.net/?f=4x-3y%20%3D%2015%5C%5C3y%20%3D%204x%20-15%5C%5C%5Cfrac%7B3y%7D%7B3%7D%20%3D%20%5Cfrac%7B4x-15%7D%5B3%7D%5C%5Cy%20%3D%20%5Cfrac%7B4%7D%7B3%7Dx%20-%20%5Cfrac%7B15%7D%7B3%7D%5C%5C%20y%20%3D%20%5Cfrac%7B4%7D%7B3%7Dx%20-%205)
Let m1 be the slope of given line
then
m1 = 4/3
Let m2 be the slope of line perpendicular to given line
As we know that the product of slopes of two perpendicular line is -1
![m_1.m_2 = -1\\\frac{4}{3} . m_2 = -1\\m_2= -\frac{3}{4}](https://tex.z-dn.net/?f=m_1.m_2%20%3D%20-1%5C%5C%5Cfrac%7B4%7D%7B3%7D%20.%20m_2%20%3D%20-1%5C%5Cm_2%3D%20-%5Cfrac%7B3%7D%7B4%7D)
Equation of line is given by:
![y = m_2x+b](https://tex.z-dn.net/?f=y%20%3D%20m_2x%2Bb)
Putting the value of the slope
![y = -\frac{3}{4}x +b](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B4%7Dx%20%2Bb)
Putting the point (8,-5) in equation
![-5 = -\frac{3}{4} (8) +b\\-5 = -3 * 2 +b\\-5 = -6 +b\\b = -5+6\\b = 1](https://tex.z-dn.net/?f=-5%20%3D%20-%5Cfrac%7B3%7D%7B4%7D%20%288%29%20%2Bb%5C%5C-5%20%3D%20-3%20%2A%202%20%2Bb%5C%5C-5%20%3D%20-6%20%2Bb%5C%5Cb%20%3D%20-5%2B6%5C%5Cb%20%3D%201)
Putting the value of b in equation
![y = -\frac{3}{4}x +1](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B4%7Dx%20%2B1)
Hence,
The equation of line perpendicular to given line passing through (8,-5) is:
![y = -\frac{3}{4}x +1](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B3%7D%7B4%7Dx%20%2B1)
Keywords: Equation of line, slope
Learn more about equation of line at:
#LearnwithBrainly
K=4
add seven on both sides
2x-4y=7
add 4y on both sides
2x=7+4y
divide 2 on both sides
x=7+4y/2
plug that into original equation
2(7+4y/2)-4y-7=0
7 and 4y cancel out
2(2)=0
4=0
Hi! Can you please be more clear on your question?