Question

find the slope of the line that passes through (7, 4) and (4, 6). simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Let \((x_1, y_1)=(7, 4)\) and \((x_2, y_2)=(4, 6)\).

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{6 - 4}{4 - 7} \).

Step4: Simplify numerator and denominator

Simplify the numerator: \( 6 - 4 = 2 \). Simplify the denominator: \( 4 - 7=-3 \). So \( m = \frac{2}{-3}=-\frac{2}{3} \).

Answer:

\(-\frac{2}{3}\)