1. **Problem:** Convert the line passing through points $(7, -1)$ and $(8, 2)$ into standard form and general form. 2. **Formula:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ The slope-intercept form is: $$y = mx + b$$ The standard form is: $$Ax + By = C$$ where $A$, $B$, and $C$ are integers, and $A \geq 0$. 3. **Calculate slope:** $$m = \frac{2 - (-1)}{8 - 7} = \frac{3}{1} = 3$$ 4. **Find $b$ (y-intercept):** Use point $(7, -1)$: $$-1 = 3 \times 7 + b$$ $$-1 = 21 + b$$ $$b = -1 - 21 = -22$$ 5. **Slope-intercept form:** $$y = 3x - 22$$ 6. **Convert to standard form:** Move all terms to one side: $$y - 3x = -22$$ Rewrite as: $$-3x + y = -22$$ Multiply both sides by $-1$ to make $A$ positive: $$3x - y = 22$$ 7. **General form:** The general form is the same as standard form but often written as: $$Ax + By + C = 0$$ Rewrite: $$3x - y - 22 = 0$$ **Final answers:** - Standard form: $$3x - y = 22$$ - General form: $$3x - y - 22 = 0$$ This process can be applied similarly to other points or slope-intercept parameters.