Question

finding slope from two points
find the slope of the line through each pair of points.

1. (19, -16), (-7, -15) 2) (1, -19), (-2, -7)
2. (-4, 7), (-6, -4) 4) (20, 8), (9, 16)
3. (17, -13), (17, 8) 6) (19, 3), (20, 3)
4. (3, 0), (-11, -15) 8) (19, -2), (-11, 10)

Explanation:

Problem 1: $(19, -16), (-7, -15)$

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1 = 19, y_1=-16, x_2=-7, y_2 = -15 \).

Step2: Substitute values into formula

\( m=\frac{-15 - (-16)}{-7 - 19}=\frac{-15 + 16}{-26}=\frac{1}{-26}=-\frac{1}{26} \)

Step1: Identify coordinates

\( x_1 = 1, y_1=-19, x_2=-2, y_2 = -7 \). Use slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Calculate slope

\( m=\frac{-7 - (-19)}{-2 - 1}=\frac{-7 + 19}{-3}=\frac{12}{-3}=-4 \)

Step1: Define points

\( x_1=-4, y_1 = 7, x_2=-6, y_2=-4 \). Apply slope formula.

Step2: Compute slope

\( m=\frac{-4 - 7}{-6 - (-4)}=\frac{-11}{-6 + 4}=\frac{-11}{-2}=\frac{11}{2} \)

Answer:

\( -\frac{1}{26} \)

Problem 2: $(1, -19), (-2, -7)$