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This problem trains for: SAT-I, AMC-8, GMAT.

If the slope of a line is doubled and its y-intercept is halved, the point (4, 7) is a fixed point (belongs to the line before as well as after the transformation). What is the equation of the line?

Let the line have the expression:

equation

After doubling the slope and halving the y-intercept, the transformed line has the expression:

equation

The point (4, 7) is fixed:

equation

equation

Solve the system for m and n:

equation

equation

equation

equation

equation

equation

equation

equation