Question

Find equation of line which passes through (4, 6) and perpendicular on the

line having equation x – 3y = 8.​

Answer 1

Answer:

3x + y - 18 = 0

Step-by-step explanation:

Given,

A = (4 , 6)

x - 3y = 8

To Find :-

Equation of line which passes through (4, 6) and perpendicular on the line having equation x - 3y = 8.​

How To Do :-

We need to find the slope of the given line by converting the line into 'y = mx + c' form after finding the slope we need to apply the condition of perpendicularity and a formula to find the line equation.

Formula Required :-

1) If two lines are perpendicular then their product of the slopes = - 1

2) Slope in 'y = mx + c' = 'm'.

3) If (x_1 , y_1) are the given co-ordinates of the points and 'm' is slope then the equation of line is :-

y - y_1 = m(x - x_1)

Solution :-

Taking the line :-

x - 3y = 8

x - 8 = 3y

y = (x - 8)/3

y = x/3 - 8/3

y = 1(x)/3 - 8/3

∴ It is in form of 'y = mx + c' :-

→ Slope = 1/3

Let ,the slope be 'm_1' :- → m_1 = 1/3

The required slope be 'm_2'

→ m_1 × m_2 = - 1

[ ∴ Product of 2 perpendicular slopes = - 1]

→ 1/3 × m_2 = - 1

m_2 = - 1 × 3

m_2 = - 3  

Using the formula 'y - y_1 = m(x - x_1)'  to find the line :-

(4 , 6)

Let,

x_1 = 4 , y_1 = 6

m_2 = m = - 3

y - 6 = - 3(x - 4)

y - 6 = - 3x + 12

y - 6 + 3x - 12 = 0

3x + y - 18 = 0

∴ '3x + y - 18 = 0' is the line which passes through (4, 6) and perpendicular on the line having equation x - 3y = 8.​