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.
[tex]-6y-7=-x[/tex]
Add both sides by 7.
[tex]-6y=-x+7[/tex]
Divide both sides by -6.
[tex]y= \frac{1}{6} x- \frac{7}{6} [/tex]
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 reciprocal 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 [tex](x_1,y_1)[/tex], the point slope form equation is the following:
[tex]y-y_1=m(x-x_1)[/tex]
We know the passing point and the slope. Now, let's plug them into the point-slope form formula.
[tex]y-(-9)= -6(x-6)[/tex]
[tex]y+9= -6(x-6)[/tex]
That is your answer for the point-slope form equation.
To change this to general form, distribute first.
[tex]y+9= -6x+36[/tex]
Add both sides by [tex]6x[/tex] and subtract both sides by 36.
[tex]6x+y-27=0[/tex]
That's your answer for the general form equation.
I hope this helps and have an awesome day! :)
