Daniel L. answered • 04/09/16

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Hi r,

You have a short name.

Parallel lines have the same slope. So you need to find the slope of the parallel line and then plug in the X and Y values of the point in the new line's equation to solve for the Y intercept.

So let's first rewrite the parallel line's equation into slope intercept form (y = mx + b) where m is the slope and b is the y intercept (where the line meets the Y axix).

2x + 3y = 12

Subtract 2x from each side--> 3y = 12 - 2x

Divide each side by 3--> y = -2x/3 + 12

So the slope is -2/3.

The new line's equation is y - -2x/3 + b

Plug in the coordinates--> 6 = (-2)(2)/3 + b

6 = -4/3 + b

b = 6 + 4/3 = 18/3 + 4/3 = 22/3

So now we know the equation of the line: y = -2x/3 + 22/3

Dan