The figure below shows road accessibility on the \(X\)-axis and hierarchy of roads on the \(Y\)-axis. The line which represents their correct relationship is .
Show Hint
Higher-order roads (expressways) are built for mobility and kept low on accessibility; lower-order roads (local streets) are built for accessibility, so hierarchy and accessibility move in opposite directions.
Step 1: Understanding the Question:
The figure plots road accessibility (how easily vehicles can enter or exit a road) on the \(X\)-axis, from low to high, against the hierarchy of roads (from local street at the bottom up to expressway at the top) on the \(Y\)-axis. Four candidate lines are marked \(P\), \(Q\), \(R\), and \(S\), and we need to pick the one that matches the true relationship between these two variables.
Step 2: Key Formula or Approach:
In transportation and urban planning, road hierarchy is built on a trade-off called the mobility versus access principle: roads higher in the hierarchy, expressways and highways, are designed to move traffic fast over long distances, so they deliberately restrict the number of access points along their length, giving them low accessibility. Roads lower in the hierarchy, collector roads and local streets, exist mainly to give direct property access, so they carry less through traffic but allow high accessibility. This means, as accessibility rises from low to high, road hierarchy must fall from expressway down to local street: a consistent downward relationship across the whole range, not a rising line and not a flat line.
Step 3: Detailed Explanation:
Checking each labeled line against this rule: a line that rises from lower-left to upper-right, as marked at \(R\), would mean hierarchy increases as accessibility increases, the opposite of the real relationship, so it is wrong. A line that stays roughly flat across the accessibility range, as marked at \(P\), would mean hierarchy does not depend on accessibility at all, which also contradicts the accepted principle, so it is wrong. Of the downward-sloping portions in the figure, the segment marked \(Q\) only traces a short drop near the low-accessibility end and does not represent the trade-off across the practical range the question is asking about. The segment marked \(S\) traces the full range consistently, from high hierarchy at low accessibility down to low hierarchy at high accessibility, matching the accepted road-hierarchy versus accessibility trade-off.
Step 4: Final Answer:
The correct line representing the relationship between road accessibility and road hierarchy is \(S\): as accessibility increases, road hierarchy decreases.
