Relationship between traffic speed and density is described using a negatively sloped straight line. If \( v_f \) is the free-flow speed, then the speed at which the maximum flow occurs is:
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In traffic flow theory, maximum flow occurs when the traffic speed is half of the free-flow speed for a linearly decreasing speed-density relationship.
For a negatively sloped speed-density curve, the maximum flow occurs when the speed is half of the free-flow speed \( v_f \). This is a standard result from traffic flow theory.
Final Answer:
\[
\boxed{\frac{v_f}{2}}.
\]
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