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(1,4) and B(5,1). Y-values: 4 (A), 1 (B).

Step2: Identify x-values of points

X-values: 1 (A), 5 (B).

Step3: Form change in y and x

Change in y: \( 1 - 4 \) (or \( 4 - 1 \) with sign), change in x: \( 5 - 1 \). So expression is \( \frac{1 - 4}{5 - 1} \) (or \( \frac{4 - 1}{1 - 5} \), but slope formula is \( \frac{y_2 - y_1}{x_2 - x_1} \), so using B - A: \( \frac{1 - 4}{5 - 1} \) or A - B: \( \frac{4 - 1}{1 - 5} \), but the boxes are for numerator (y) and denominator (x) differences. So numerator: \( 1 - 4 \) (or \( 4 - 1 \)) and denominator: \( 5 - 1 \) (or \( 1 - 5 \)). Taking B - A: numerator \( 1 - 4 \), denominator \( 5 - 1 \).

Answer:

\(\frac{1 - 4}{5 - 1}\) (or \(\frac{4 - 1}{1 - 5}\), but the correct fill based on points B(5,1) and A(1,4) for slope formula \( \frac{y_B - y_A}{x_B - x_A} \) is \(\frac{1 - 4}{5 - 1}\), so numerator: \(1 - 4\), denominator: \(5 - 1\))