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

Points A(1,8) and B(6,2) have y-values 8 and 2.

Step2: Identify x-values

Their x-values are 1 and 6.

Step3: Form change expressions

Change in y: \( 2 - 8 \) (or \( 8 - 2 \), but order matters for slope direction; here using B - A).
Change in x: \( 6 - 1 \).
So the expression is \( \frac{2 - 8}{6 - 1} \) (or \( \frac{8 - 2}{1 - 6} \), but matching the slope formula's change in y over change in x with correct order).

Answer:

\(\frac{2 - 8}{6 - 1}\) (or \(\frac{8 - 2}{1 - 6}\), but filling the boxes as \(2 - 8\) over \(6 - 1\) or \(8 - 2\) over \(1 - 6\); typically \(8 - 2\) and \(6 - 1\) for positive run, so \(\frac{8 - 2}{6 - 1}\) is also correct. The boxes should be filled with 8, 2, 6, 1 (or 2, 8, 1, 6 depending on direction, but standard is \(y_2 - y_1\) over \(x_2 - x_1\) where B is \((x_2,y_2)\) and A is \((x_1,y_1)\), so \(2 - 8\) and \(6 - 1\) or \(8 - 2\) and \(1 - 6\). The correct filling for the boxes is top: 8, 2 (or 2, 8) and bottom: 6, 1 (or 1, 6). So the expression is \(\frac{8 - 2}{6 - 1}\) (most common as positive run) or \(\frac{2 - 8}{6 - 1}\).)