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

Use the given conditions to write an equation for the line in​ point-slope form and-example-1
User Eos
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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= (1)/(6) x- (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! :)
User GlassHalfAwesome
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