noun, noun which may take the genitive case particle 'no'
on a line; on the line
Literal spatial meaning: located on a line, such as a drawn line, a route, or a boundary line.
The dots are lined up on the line.
この線上をまっすぐ歩いてください。
Please walk straight along this line.
on the borderline; on the verge; on the brink
Figurative use: at a critical dividing point between two states, often with 〜の線上 or 〜線上にある.
His proposal is on the borderline of feasibility.
The negotiations are on the verge of breaking down.
on the extension of a line; as an extension of
on the verge of starvation; at the point of starving
Compound of 線 (line) and 上 (on/above). The figurative sense developed from the spatial meaning.