Question

Find the equation of the line through point (−5,5) and perpendicular to y=5/9x−4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 1/2).

Answer 1

`y = -9/5x-4`

Explanation:

Given

Passes through
`(-5,5)`

Perpendicular to
`y = 5/9x - 4`

Required

The line equation

First, we calculate its slope (m)

In
`y = 5/9x - 4`, the slope is:

`m =5/9`

This is so because, the gradient intercept is:

`y = mx + b`

By comparison, you have:
`m =5/9`

Since the required line and
`y = 5/9x - 4` are perpendicular, then the slope (m2) is:

`m_2 = -1/m`

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

`m_2 = -9/5`

The equation is then calculated using:

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

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

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

`y = -9/5x-9 + 5`

`y = -9/5x-4`