Question

the coordinates of two points on a line are (-6, 5) and (3, -2). find the slope of the line.
\\(\frac{9}{7}\\)
\\(\frac{7}{9}\\)
\\(-\frac{9}{7}\\)
\\(-\frac{7}{9}\\)

Explanation:

Step1: Recall slope formula

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

Step2: Identify coordinates

Let \((x_1, y_1)=(-6, 5)\) and \((x_2, y_2)=(3, -2)\).

Step3: Substitute into formula

Substitute values: \( m=\frac{-2 - 5}{3 - (-6)}=\frac{-7}{9}=-\frac{7}{9} \).

Answer:

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