# How Does a "Bonding Curve" Visually Represent the X Y = K Relationship? ⎊ Path

**Published:** 2025-12-05
**Author:** Greeks.live
**Categories:** Path

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## How Does a “Bonding Curve” Visually Represent the X Y = K Relationship?

A bonding curve is a graph where the x-axis represents the reserve of one token (x) and the y-axis represents the reserve of the other token (y). The x × y = k formula produces a hyperbolic curve.

Any point on this curve represents a valid state of the pool, and the movement along the curve during a trade visually represents the price change and the resulting token ratio adjustment.

- [How Does a Change in the Value of “K” Affect the Pool’s Price Curve?](https://learn.greeks.live/path/how-does-a-change-in-the-value-of-k-affect-the-pools-price-curve/)

- [What Is “Slippage” and How Does It Affect the Execution of a Large Trade on an AMM?](https://learn.greeks.live/path/what-is-slippage-and-how-does-it-affect-the-execution-of-a-large-trade-on-an-amm/)

- [How Does the Concept of a “Bonding Curve” Generalize the Constant Product and Constant Sum Models?](https://learn.greeks.live/path/how-does-the-concept-of-a-bonding-curve-generalize-the-constant-product-and-constant-sum-models/)

- [Why Does the Price of a Large Trade Deviate More Significantly from the Spot Price Y/x?](https://learn.greeks.live/path/why-does-the-price-of-a-large-trade-deviate-more-significantly-from-the-spot-price-y-x/)

- [How Can a DAO Use Inverse Perpetual Swaps to Manage Risk on non-USD Denominated Assets?](https://learn.greeks.live/path/how-can-a-dao-use-inverse-perpetual-swaps-to-manage-risk-on-non-usd-denominated-assets/)

- [What Is a “Volatility Smile” and What Does It Indicate about the Black-Scholes Model’s Assumptions?](https://learn.greeks.live/path/what-is-a-volatility-smile-and-what-does-it-indicate-about-the-black-scholes-models-assumptions/)

- [Why Is the Price in an X Y=k Pool Always Quoted as the Ratio of the Reserves, Y/x?](https://learn.greeks.live/path/why-is-the-price-in-an-x-yk-pool-always-quoted-as-the-ratio-of-the-reserves-y-x/)

- [What Is a “Futures Curve” and How Is It Constructed?](https://learn.greeks.live/path/what-is-a-futures-curve-and-how-is-it-constructed/)

## Glossar

### [Bonding Curve](https://learn.greeks.live/area/bonding-curve/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)

Mechanism ⎊ Bonding Curve describes a mathematical function that algorithmically determines the price of a token based on its supply.

## Discover More

### [Can ERC-20 Tokens Represent Ownership of a Physical Asset?](https://learn.greeks.live/path/can-erc-20-tokens-represent-ownership-of-a-physical-asset/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Can ERC-20 Tokens Represent Ownership of a Physical Asset?](https://learn.greeks.live/wp-content/uploads/2025/10/Intersecting-Translucent-Hedging-Vectors-Over-Centralized-Decentralized-Finance-Wheel-Mechanism.webp)

Yes, they can represent pooled or fractional ownership of physical assets (tokenization), but not unique individual assets.

### [In Financial Terms, How Does a 'Share' Represent a Miner's Fractional Claim on the Expected Block Reward?](https://learn.greeks.live/path/in-financial-terms-how-does-a-share-represent-a-miners-fractional-claim-on-the-expected-block-reward/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![In Financial Terms, How Does a 'Share' Represent a Miner's Fractional Claim on the Expected Block Reward?](https://learn.greeks.live/wp-content/uploads/2025/10/Quantum-Entanglement-Visualization-Representing-High-Frequency-Crypto-Derivatives-Settlement-Mechanics.webp)

A unit of work that is a probabilistic fractional claim on the pool's next block reward, used for proportional distribution.

### [Does the Relationship Hold True for Futures on Assets That Do Not Require Physical Storage, like Non-Dividend-Paying Stocks?](https://learn.greeks.live/path/does-the-relationship-hold-true-for-futures-on-assets-that-do-not-require-physical-storage-like-non-dividend-paying-stocks/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![Does the Relationship Hold True for Futures on Assets That Do Not Require Physical Storage, like Non-Dividend-Paying Stocks?](https://learn.greeks.live/wp-content/uploads/2025/10/Quantum-Entanglement-Mechanism-Within-A-Hardware-Wallet-Securing-Digital-Asset-Derivatives-Contracts.webp)

Yes, the relationship simplifies as the cost of carry is reduced solely to the financing cost (risk-free rate) since storage and income are zero.

### [How Do 'Storage Costs' Affect the Relationship between Futures and Spot Prices?](https://learn.greeks.live/path/how-do-storage-costs-affect-the-relationship-between-futures-and-spot-prices/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Do 'Storage Costs' Affect the Relationship between Futures and Spot Prices?](https://learn.greeks.live/wp-content/uploads/2025/10/Macro-View-of-Centralized-Exchange-Lens-Reflecting-Multi-Asset-Volatility-Surface-Dynamics.webp)

Storage costs are part of the 'cost of carry' and typically cause the futures price to be higher than the spot price in a normal market (contango).

### [What Is the Relationship between Interest Rates and Option Premium?](https://learn.greeks.live/path/what-is-the-relationship-between-interest-rates-and-option-premium/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Relationship between Interest Rates and Option Premium?](https://learn.greeks.live/wp-content/uploads/2025/10/Concrete-Truss-Structure-Intersecting-Spherical-Boundaries-Within-Decentralized-Finance-Mechanism-Rendering.webp)

Higher interest rates slightly increase call premiums and slightly decrease put premiums due to changes in the cost of carry.

### [How Does the Relationship between Historical Volatility and Implied Volatility Inform a Trading Strategy?](https://learn.greeks.live/path/how-does-the-relationship-between-historical-volatility-and-implied-volatility-inform-a-trading-strategy/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![How Does the Relationship between Historical Volatility and Implied Volatility Inform a Trading Strategy?](https://learn.greeks.live/wp-content/uploads/2025/10/Symmetric-Abstract-Visualization-of-Decentralized-Autonomous-Organization-Governance-Mechanism-Structure.webp)

Comparing HV (past) and IV (expected future) helps traders determine if an option is currently cheap or expensive for volatility trading.

### [What Is the Relationship between an option'S'moneyness' and Its Time Value?](https://learn.greeks.live/path/what-is-the-relationship-between-an-options-moneyness-and-its-time-value/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Relationship between an option'S'moneyness' and Its Time Value?](https://learn.greeks.live/wp-content/uploads/2025/10/Crystalline-Geometric-Abstraction-Illustrating-Convexity-Skew-in-Decentralized-Finance-Derivatives-Structures.webp)

Time value is highest for at-the-money options; it decreases as options move deep in-the-money or deep out-of-the-money.

### [What Is the Relationship between Cash Settlement and a Derivative's Margin Requirements?](https://learn.greeks.live/path/what-is-the-relationship-between-cash-settlement-and-a-derivatives-margin-requirements/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Relationship between Cash Settlement and a Derivative's Margin Requirements?](https://learn.greeks.live/wp-content/uploads/2025/10/Microscopic-View-of-Option-Contract-Hinge-Point-Near-Teal-Liquidity-Pool-Boundary.webp)

Cash settlement allows for higher leverage and lower capital outlay because margin only covers potential loss, not full notional value.

### [What Is the Relationship between Vega and the Skew in a Risk Reversal?](https://learn.greeks.live/path/what-is-the-relationship-between-vega-and-the-skew-in-a-risk-reversal/?utm_source=crypto.greeks.live&utm_medium=referral&utm_campaign=satellite)
![What Is the Relationship between Vega and the Skew in a Risk Reversal?](https://learn.greeks.live/wp-content/uploads/2025/10/Symmetrical-Bifurcation-Highlighting-Layered-Asset-Structures-in-Decentralized-Finance-Oracles.webp)

Vega measures sensitivity to absolute IV change; the trade is primarily a bet on the relative IV change (the skew).

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**Original URL:** https://learn.greeks.live/learn/how-does-a-bonding-curve-visually-represent-the-x-y-k-relationship/
