Respuesta :
Answer:
2
Step-by-step explanation:
The given equation of line is
[tex]3x+6y=-18[/tex]
We need to find the slope of a line which is perpendicular to the given line.
The given equation can be rewritten as
[tex]3x+6y+18=0[/tex] ...(i)
If a line is defined as [tex]ax+bx+c=0[/tex], then the slope of the line is
[tex]m=-\dfrac{a}{b}[/tex]
In equation (i), a=3, b=6 and c=18. So, slope of the line is
[tex]m_1=-\dfrac{3}{6}=-\dfrac{1}{2}[/tex]
Let [tex]m_2[/tex] be the slope of perpendicular line.
We know that product of two perpendicular line is -1.
[tex]m_1\cdot m_2=-1[/tex]
[tex](-\dfrac{1}{2})\cdot m_2=-1[/tex]
Multiply both sides by -2.
[tex]m_2=2[/tex]
Therefore, the slope of perpendicular line is 2.
