> [!summary] The rate of change tells you how one quantity changes with respect to another > **Key equation:** > Rate of change: $\frac{y_{2} - y_{1}}{x_{2}- x_{1}} = \frac{\Delta y}{\Delta x}$ >[!info]+ Read Time **⏱ 1 min** # Definition The rate of change is a tool to tell you how quickly one quantity changes in response to another. In math and physics, our notion can be defined differently, but they all mean the same thing. $ \frac{y_{2} - y_{1}}{x_{2}- x_{1}} = \frac{\Delta y}{\Delta x} $ ![[roc_1.png]] > [!note] Explanation Example of rate of change showing the change in ($x_{2},y_{2}$) and ($x_{1},y_{1}$) ## Logical Justification The equation can argue why this equation is true from the graph above. To find the change between $x_{2},y_{2}$ and $x_{1},y_{1}$, from the graph it can be seen that the change should be positive, and the change should be some number, since visually there is a change. So the easiest way to determine that is to see the change in the y direction and the changes in the x direction. The magnitude of the change is each quantity divided by the other. # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/lQRiw264bnI?si=OKsmU-WhxaKI5RVp" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 🧠 Enjoy this walkthrough? [Support Math & Matter](https://github.com/rajeevphysics/Obsidian-MathMatter) with a star and help others learn more easily. ---