Question

What is the equation of the line perpendicular to `y=-3/11x` that passes through `(8,7)`?

Answer 1

3y - 11x +67 = 0

Explanation:

The equation of the line is of the form : y - b = m(x - a )

where m represents the gradient and (a,b) a point on the line.

Here (a , b) =(8 , 7) is given but require m.

When 2 lines are perpendicular to each other, the product of

their gradients is - 1 .

`m_1.m_2 = -1`

let `m_1 = - 3/11 color(black)( " the gradient of given line ")`

then `m_2 color(black)(" is gradient of perpendicular line")`

hence `m_2 = -1/m_1 =( -1)/(-3/11) = 11/3`

equation : y - 7 `= 11/3 ( x - 8 )`

(multiply by 3 to eliminate fraction )

hence 3 y - 21 = 11x - 88 `rArr3 y - 11x + 67 = 0`