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Rewriting the equation of the given line in slope-intercept form,
[tex]3x+6y=18\\\\x+2y=6\\\\2y=-x+6\\\\y=-\frac{1}{2}x+3[/tex]
This means the slope of the given line is -1/2.
As perpendicular lines have slopes that are negative reciprocals, the answer is 2.
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Determine the slope of the line perpendicular to 3x+6y=18
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\bf{\dfrac{3}{6}x+\dfrac{6}{6}y=\dfrac{18}{6}[/tex] | dividing the ENTIRE equation by 6, to make it easier to write in y=mx+b form
[tex]\bf{\dfrac{1}{2}x+y=3}[/tex] | subtract 1/2 x
[tex]\bf{y=-\dfrac{1}{2}x+3[/tex].
[tex]\cline{1-2}[/tex]
Now, perpendicular lines' slopes are opposite inverses of each other.
The opposite inverse of -1/2 is
= 2
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=2}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]