Key property: Work by gravity is PATH-INDEPENDENT. It depends only on the vertical displacement (change in height).

$W_{gravity}$ = -mg * $delta_h$ = mg($h_{initial}$ - $h_{final}$)

Where $delta_h$ = $h_{final}$ - $h_{initial}$.

Going down by h: $W_{gravity}$ = +mgh (gravity does positive work) Going up by h: $W_{gravity}$ = -mgh (gravity does negative work)

For any curved path: Only the vertical component of displacement matters. Along a curved incline of length L at angle theta: h = Lsin(theta) $W_{gravity}$ = mgLsin(theta)

This path independence is precisely what makes gravity a conservative force. Friction work DOES depend on path length, making friction non-conservative.