Question

Find an equation for the line in the form of ax+by=c where a,b,c are interferes with no common to all three and a. Through (3,-9), perpendicular to x+y=6

Answer 1

Answer:

The equation for the line in the form of $ax+by=c$ is $x-y=12$

Step-by-step explanation:

Given point is $(3,-9)$. And equation of perpendicular line is $x+y=6$

First, we will slope of line $x+y=6$. Let us call it $m_1$.

$x+y=6\\y=-x+6\\y=mx+c$

$m_1=-1$, that is slope of line $x+y=6$.

Let us call slope of line perpendicular to x+y=6 is $m_2$ .

We know,

$m_1\times m_2=-1\\m_2=\frac{-1}{m_1}$

$m_2=\frac{-1}{-1}=1$

So, the slope of line perpendicular to $x+y=6$ is $1$

Also, the line passes through point $(3,-9)$

$(y-y_1)=m(x-x_1)\\(y-(-9))=1(x-3)\\y+9=x-3\\y=x-3-9\\y=x-12\\x-y=12$

So, the equation for the line in the form of $ax+by=c$ is $x-y=12$