The slope intercept form: [tex]y=mx+b[/tex]
m - a slope
We have:
[tex]6x+3y=-9[/tex] |subtract 6x from both sides
[tex]3y=-6x-9[/tex] |divide both sides by 3
[tex]y=-2x-3[/tex]
[tex]k:\ y=m_1x+b_1\\l:\ y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1[/tex]
[tex]k:\ y=-2x-3\to m_1=-2\\l:\ y=mx+b\to m_2=m[/tex]
substitute
[tex]-2m=-1[/tex] |divide both sides by (-2)
[tex]\boxed{m=0.5}[/tex]
Answer: The slope of a line perpendicular to 6x + 3y = -9 is equal 0.5.
