Respuesta :
Answer:
The equation for the line in the form of [tex]ax+by=c[/tex] is [tex]x-y=12[/tex]
Step-by-step explanation:
Given point is [tex](3,-9)[/tex]. And equation of perpendicular line is [tex]x+y=6[/tex]
First, we will slope of line [tex]x+y=6[/tex]. Let us call it [tex]m_1[/tex].
[tex]x+y=6\\y=-x+6\\y=mx+c[/tex]
[tex]m_1=-1[/tex], that is slope of line [tex]x+y=6[/tex].
Let us call slope of line perpendicular to x+y=6 is [tex]m_2[/tex] .
We know,
[tex]m_1\times m_2=-1\\m_2=\frac{-1}{m_1}[/tex]
[tex]m_2=\frac{-1}{-1}=1[/tex]
So, the slope of line perpendicular to [tex]x+y=6[/tex] is [tex]1[/tex]
Also, the line passes through point [tex](3,-9)[/tex]
[tex](y-y_1)=m(x-x_1)\\(y-(-9))=1(x-3)\\y+9=x-3\\y=x-3-9\\y=x-12\\x-y=12[/tex]
So, the equation for the line in the form of [tex]ax+by=c[/tex] is [tex]x-y=12[/tex]
