Question

use the coordinates of points a and b to write an expression to represent the slope of the line. point a : (2, 5) point b : (12, 7) slope = \frac{vertical distance}{horizontal distance} = \frac{\square - \square}{\square - \square}

Explanation:

Step1: Recall slope formula

Slope is vertical change (change in y) over horizontal change (change in x), so \( \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

For Point A \((2, 5)\) and Point B \((12, 7)\), \( y_2 = 7 \), \( y_1 = 5 \), \( x_2 = 12 \), \( x_1 = 2 \).

Step3: Substitute into formula

Vertical distance (change in y) is \( 7 - 5 \), horizontal distance (change in x) is \( 12 - 2 \). So the expression is \( \frac{7 - 5}{12 - 2} \).

Answer:

\(\frac{7 - 5}{12 - 2}\)