Question

Use the given conditions to write an equation for the line in​ point-slope form and in​ general form.

Answer 1

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.

$-6y-7=-x$

Add both sides by 7.

$-6y=-x+7$

Divide both sides by -6.

$y= \frac{1}{6} x- \frac{7}{6}$

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 $(x_1,y_1)$, the point slope form equation is the following:

$y-y_1=m(x-x_1)$

We know the passing point and the slope. Now, let's plug them into the point-slope form formula.

$y-(-9)= -6(x-6)$
$y+9= -6(x-6)$

That is your answer for the point-slope form equation.
To change this to general form, distribute first.

$y+9= -6x+36$

Add both sides by $6x$ and subtract both sides by 36.

$6x+y-27=0$

That's your answer for the general form equation.
I hope this helps and have an awesome day! :)