Need help with the problem noted above equation (3,9) that is parallel to 2x+3y=16

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First solve for y

2x+3y=16 (subtract by 2x to both sides)

3y=-2x+16 (divide by )

y=-2/3x+16/3

Thus we know the slope is m=-2/3x

Since parallel lines share the same slope, we know that m=-2/3x for the other line.

Now we can use point slope formula with the point (3,9)

Point-slope form

y-y_1=m(x-x_1)

y-9=-2/3(x-3)

Put in standard form

y-9=-2/3x-2 (add nine to both sides)

y=-2/3x+7.

Thus the parallel line equation is

y=-2/3x+7

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