Question 647772
When you're given a specific point and an equation, you can use the point-slope formula to find a parallel line. REMEMBER: Parallel lines will always have the same slope as to what they gave you.

The point-slope formula is: y – y1 = m(x – x1)

First of all, the equation you provided is not in standard form. You need to put this equation in standard form to be able to obtain its slope. 

The slope-intercept form (standard form) of an equation can be expressed as:

{{{y = mx + b}}}

Step 1: We must put the equation they gave us in standard form, like the one that is above.

Original equation: {{{2x-3y=7}}}

You want to get 'y' by itself, so subtract '2x' from both sides.

Step 2: You'll get:

{{{-3y=-2x+7}}}

We want to get 'y' by itself, so divide 3 from the 'y' and from the rest of the equation.

Step 3: It becomes: 

{{{y=2x/3-7/3}}}

Step 4: The equation originally given is now in slope-intercept form, and we now know the slope is {{{M = 2/3}}}

We know the slope stays the same as the original equation because parallel slopes stay exactly the same.

We now need to use the point-slope formula to find a parallel equation.

Let's recap.. the point-slope formula is:  y – y1 = m(x – x1) 

We're going to replace 'x1' with the 'x' coordinate given to us, the 'y1' with the 'y' coordinate given to us, and the m with the slope we just found.

Step 1: 

Original point: (8,-6)
Slope: {{{M = 2/3}}}

Let's begin by replacing the values in.

(y – (-6)) = 2/3(x – 8)

Step 2: Simplify the first parenthesis

(y + 6)) = 2/3(x – 8)

Step 3: Distribute terms

(y + 6)) = ((2x/3) - (16/3))

Step 4: Combine like terms (You want to get 'y' by itself, so subtract 6 on both sides.)

{{{y = ((2x/3) - (16/3)-(6/1))}}}

Step 5: Find an LCD (least common denominator) that will divide into both denominators. The LCD is 3, so multiply 6 by 3 on the top and on the bottom.

{{{y = ((2x/3) - (16/3)-(18/3))}}}

Step 6: Combine like terms (subtract the fractions)

{{{y = ((2x/3) - (34/3))}}}

Your new parallel equation is: {{{y = ((2x/3) - (34/3))}}}