Question

Through: (-5, -3), perp. to y=-9/4x-5

Answer 1

Given:

A line passes through (-5,-3) and perpendicular to
`y=-(9)/(4)x-5`.

To find:

The equation of the line.

Solution:

We have,

`y=-(9)/(4)x-5`

On comparing this equation with slope intercept form, i.e.,
`y=mx+b`, we get

`m_2=-(9)/(4)`

It means, slope of this line is
`-(9)/(4)`.

Product of slopes of two perpendicular lines is always -1.

`m_1* m_2=-1`

`m_1 * \left(-(9)/(4)\right)=-1`

`m_1=(4)/(9)`

Slope of required line is
`(4)/(9)` and it passes through the point (-5,-3). So, the equation of the line is

`y-y_1=m(x-x_1)`

where, m is slope.

`y-(-3)=(4)/(9)(x-(-5))`

`y+3=(4)/(9)(x+5)`

`9(y+3)=4(x+5)`

`9y+27=4x+20`

`27-20=4x-9y`

`7=4x-9y`

Therefore, the equation of required line is
`4x-9y=7`.