Answer:
slope = 2
Step-by-step explanation:
Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]
(where m is the slope and b is the y-intercept)
Given equation:
[tex]3x + 6y = -54[/tex]
Rearrange the given equation to make y the subject:
[tex]\implies 6y=-3x=-54[/tex]
[tex]\implies y=-\dfrac{1}{2}x-9[/tex]
Therefore, the slope of the given equation is [tex]-\dfrac{1}{2}[/tex].
If two lines are perpendicular to each other, the product of their slopes will be -1.
Therefore, the slope (m) of the line perpendicular to the given equation is:
[tex]\implies -\dfrac{1}{2} \cdot m=-1[/tex]
[tex]\implies m=-1 \div -\dfrac{1}{2}[/tex]
[tex]\implies m=-1 \cdot-2[/tex]
[tex]\implies m=2[/tex]
