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Tangents Parallel to a Given Line

Move the value of a along the slider to see the line 9x+4x-12=0 move up and down. Look for two locations where the green line becomes tangent to the curve, note the approximate value of x.
Calculate the equations of the two tangent lines that are parallel to the line 9x+4y = -1.6. Type each equation in the input to see if you are correct.