Question

What is the equation of the line perpendicular to `y=-5/9x` that passes through `(-7,3)`?

Answer 1

5y - 9x + 48 = 0

Explanation:

One of the forms of the equation of a straight line is y = mx + c where m represents the gradient and c , the y-intercept.

the line `y = -5/9 x`

is in this form with c = 0 and m = `-5/9`

When 2 lines are perpendicular then the product of their gradients :

`m_1m_2 = - 1`

The gradient of the perpendicular line is : `-5/9 xx m_2 = - 1`

`rArr m_2 =- 1/(-5/9) = 9/5`

equation : y - b = m(x - a ) , m = `9/5 , (a , b ) = ( - 7 , 3 )`

`rArr y - 3 = 9/5 (x - 7 )`

multiply both sides by 5 to eliminate fraction : `5y - 15 = 9x - 63`

equation of perpendicular line is 5y - 9x + 48 = 0