Question

(-4, 7), (-6, -4)
(20, 8), (9, 16)
(17, -13), (17, 8)

Explanation:

Step1: Recall the 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: Calculate slope for \((-4,7)\) and \((-6,-4)\)

Let \((x_1,y_1)=(-4,7)\) and \((x_2,y_2)=(-6,-4)\). Then \( m=\frac{-4 - 7}{-6-(-4)}=\frac{-11}{-2}=\frac{11}{2} \).

Step3: Calculate slope for \((20,8)\) and \((9,16)\)

Let \((x_1,y_1)=(20,8)\) and \((x_2,y_2)=(9,16)\). Then \( m=\frac{16 - 8}{9 - 20}=\frac{8}{-11}=-\frac{8}{11} \).

Step4: Calculate slope for \((17,-13)\) and \((17,8)\)

Let \((x_1,y_1)=(17,-13)\) and \((x_2,y_2)=(17,8)\). Then \( m=\frac{8-(-13)}{17 - 17}=\frac{21}{0} \), which is undefined (vertical line).

Answer:

For \((-4,7),(-6,-4)\): \(\frac{11}{2}\)
For \((20,8),(9,16)\): \(-\frac{8}{11}\)
For \((17,-13),(17,8)\): Undefined