1. Let's start by understanding the problem: you want to see all the equations and how to derive them step-by-step. 2. Typically, in algebra or calculus, equations are derived using fundamental formulas and rules such as the distributive property, factoring, or differentiation. 3. For example, if we want to solve a quadratic equation $ax^2 + bx + c = 0$, we use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ This formula comes from completing the square on the quadratic expression. 4. Another example is the slope-intercept form of a line: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 5. To derive this, we start from two points $(x_1, y_1)$ and $(x_2, y_2)$ and calculate the slope: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Then use point-slope form: $$y - y_1 = m(x - x_1)$$ which simplifies to slope-intercept form. 6. If you have a specific equation or problem in mind, please provide it so I can show the exact derivation steps.