Question

What is the equation of the line that is perpendicular to `2y=-6x+8` if its `y`-intercept is `5`?

Answer 1

`y=1/3x+5`

Explanation:

Given -

`2y=-6x+8`

`y=(-6)/2 x+8/2`
`y=-3x+4`

The slope of this line is `m_1=-3`

Another line is passing through `(0, 5)`
This line is perpendicular to the line `y=-3x+4`

Find the slope of the other line -

`m_2` is the slope of the other line.

For two lines to be perpendicular -

`m_1 xx m_2 = -1`

Then

`m_2=(-1)/(-3)=1/3`

The equation is

`y=mx+c`
`y=1/3x+5`