Question

line gh contains points g(-2, 6) and h(5, -3). what is the slope of \overleftrightarrow{gh} ?
\boxed{\frac{-7}{9}} \boxed{\frac{-7}{3}}
\boxed{\frac{-9}{7}} \boxed{\frac{-3}{7}}

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1=-2 \), \( y_1 = 6 \), \( x_2 = 5 \), \( y_2=-3 \).

Step2: Substitute values into formula

Substitute the values into the slope formula:
\( m=\frac{-3 - 6}{5 - (-2)}=\frac{-9}{5 + 2}=\frac{-9}{7}=-\frac{9}{7} \)

Answer:

\(-\frac{9}{7}\) (corresponding to the option with \(-\frac{9}{7}\))