1. The problem involves understanding the variables $y_1$, $y_2$, $x_1$, and $x_2$, which typically represent coordinates of two points in a plane. 2. To find the distance between these two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the distance formula derived from the Pythagorean theorem: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. To find the slope of the line passing through these points, use the slope formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Note: The slope is undefined if $x_2 = x_1$. 4. To find the midpoint between the two points, use the midpoint formula: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ 5. These formulas help analyze the relationship between two points, such as distance, slope, and midpoint. 6. If you have specific values for $x_1$, $x_2$, $y_1$, and $y_2$, substitute them into these formulas to compute the desired quantities. This guide provides a step-by-step approach to working with $y_1$, $y_2$, $x_1$, and $x_2$ in coordinate geometry.