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This problem trains for: SAT-I, SAT-II, Math Kangaroo 9-10.

The line that has slope 0.5 and passes through the origin is reflected across the line y=x. What is the slope of the reflected line?

The line with slope 0.5 that passes through the origin has equation:

equation

The line:

equation

must bisect the angle formed by the given line and its reflection. Therefore, the reflected line and the y-axis must form an angle congruent to the angle formed by the given line and the x-axis.

figure

Thus, the slope of the reflected line is equal to the reciprocal of the slope of the given line:

equation