Question

What is the slope of a line that is perpendicular to 6x+3y=-9

Answer 1

The slope intercept form:
`y=mx+b`

m - a slope

We have:

`6x+3y=-9` |subtract 6x from both sides

`3y=-6x-9` |divide both sides by 3

`y=-2x-3`

`k:\ y=m_1x+b_1\\l:\ y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1`

`k:\ y=-2x-3\to m_1=-2\\l:\ y=mx+b\to m_2=m`

substitute

`-2m=-1` |divide both sides by (-2)

`\boxed{m=0.5}`

Answer: The slope of a line perpendicular to 6x + 3y = -9 is equal 0.5.