Question

use the coordinates to write an expression you could use to find the change in vertical distance for a given change in horizontal distance.

slope = \frac{\text{vertical distance}}{\text{horizontal distance}} = \frac{\text{change in } y\text{-values}}{\text{change in } x\text{-values}}

= \frac{\square - \square}{\square - \square}

Explanation:

Step1: Identify y-values of points

Points A(1,8) and B(6,2). Y-values: 8 (A), 2 (B).

Step2: Identify x-values of points

X-values: 1 (A), 6 (B).

Step3: Form slope expression

Slope formula: $\frac{y_2 - y_1}{x_2 - x_1}$. Substitute: $\frac{2 - 8}{6 - 1}$ (or $\frac{8 - 2}{1 - 6}$, but order matters for consistency; using B - A here as per the boxes' order, but either order with consistent subtraction works).

Answer:

$\frac{2 - 8}{6 - 1}$ (or $\frac{8 - 2}{1 - 6}$, but the first form with 2, 8, 6, 1 in the boxes as per the diagram's likely intended order of B - A for the numerator and denominator)