Respuesta :

First, let's convert the given line equation into slope-intercept form to find the slope.
Let's start converting by subtracting both sides by 3x.

[tex]-2y-5=-3x[/tex]

Add both sides by 5.

[tex]-2y=-3x+5[/tex]

Divide both sides by -2.

[tex]y= \frac{3}{2} x- \frac{5}{2} [/tex]

The slope of the equation given is 3/2. Since the point-slope form line is parallel to that, the point-slope form equation must also have a slope of 3/2.

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-8= \frac{3}{2} (x-(-8))[/tex]
[tex]y-8= \frac{3}{2} (x+8)[/tex]

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

[tex]y-8= \frac{3}{2} x+12[/tex]

Subtract both sides by [tex]\frac{3}{2} x[/tex] and 12.

[tex]- \frac{3}{2} x+y-20=0[/tex]

Multiply both sides by -2

[tex]3x-2y+40=0[/tex]

That's your answer for the general form equation.
I hope this helps and have an awesome day! :)
AprilKitties
First, simplify the equation given into slope intercept form.

slope intercept form is y = mx + b, where b is the y intercept and m is the slope.

3x - 2y - 5 = 0

I would move the 2y to the other side.

3x - 5 = 2y

Then, since y can't have a coefficient, divide everything by 2;

y = 3/2x - 5/2

So there's your slope intercept form.

Point slope form is:

[tex] y - y_{1} = m( x} - x_{1} )[/tex]

Where those with a subscript of 1 are part of the same point.

So you already known one point; -8, 8. I'll just do that as the pair with subscript 1. You know the slope as well from the slope intercept form; 3/2.

You can just plug those in. 

y - 8 = 3/2 (x + 8)

Now to change this to general form.

First, distribute 3/2 to x and 8.

y - 8 = 3/2x + 12
-3/2x + y = 20
-3/2x + y - 20 = 0

Since there are no fractions, multiply everything by 2.

-3x + 2y - 40 = 0

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