First, let's convert the given line equation into slope-intercept form to find the slope of the given equation, which will help us find the slope of the point-slope form equation.
Let's start converting by subtracting both sides by x.
![-6y-7=-x](https://tex.z-dn.net/?f=-6y-7%3D-x)
Add both sides by 7.
![-6y=-x+7](https://tex.z-dn.net/?f=-6y%3D-x%2B7)
Divide both sides by -6.
![y= \frac{1}{6} x- \frac{7}{6}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7B6%7D%20x-%20%5Cfrac%7B7%7D%7B6%7D%20)
The slope of the equation given is 1/6. Since the point-slope form line is perpendicular to that, the point-slope form equation must must have a slope that's the negative <span>reciprocal </span>of 1/6, so it must have a slope of -6.
Now, let's use point-slope form.
For a line with slope m and that passes through
![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
, the point slope form equation is the following:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
We know the passing point and the slope. Now, let's plug them into the point-slope form formula.
![y-(-9)= -6(x-6)](https://tex.z-dn.net/?f=y-%28-9%29%3D%20-6%28x-6%29)
![y+9= -6(x-6)](https://tex.z-dn.net/?f=y%2B9%3D%20-6%28x-6%29)
That is your answer for the point-slope form equation.
To change this to general form, distribute first.
![y+9= -6x+36](https://tex.z-dn.net/?f=y%2B9%3D%20-6x%2B36)
Add both sides by
![6x](https://tex.z-dn.net/?f=6x)
and subtract both sides by 36.
![6x+y-27=0](https://tex.z-dn.net/?f=6x%2By-27%3D0)
That's your answer for the general form equation.
I hope this helps and have an awesome day! :)