Question

m = \frac{y_2 - y_1}{x_2 - x_1}

1. (1,2) and (7, 9)
2. (-5, 3) and (-1,0)

1. (5,-1) and (0, 3)
2. (6,2) and (6,-5)

1. (12,5) and (9,8)
2. (-3,-7) and (-8, -1)

1. (2,-5) and (7,-5)
2. (2, ¾) and (4, ¼)

1. ( ¼, 2/3 ) and (0, 1/3)
2. (3,-5) and (0,0)

Explanation:

Problem 1: (1,2) and (7,9)

Step1: Identify \( x_1, y_1, x_2, y_2 \)

\( x_1 = 1, y_1 = 2, x_2 = 7, y_2 = 9 \)

Step2: Apply slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

\( m=\frac{9 - 2}{7 - 1}=\frac{7}{6} \)

Step1: Identify \( x_1, y_1, x_2, y_2 \)

\( x_1 = -5, y_1 = 3, x_2 = -1, y_2 = 0 \)

Step2: Apply slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

\( m=\frac{0 - 3}{-1 - (-5)}=\frac{-3}{4}=-\frac{3}{4} \)

Step1: Identify \( x_1, y_1, x_2, y_2 \)

\( x_1 = 5, y_1 = -1, x_2 = 0, y_2 = 3 \)

Step2: Apply slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

\( m=\frac{3 - (-1)}{0 - 5}=\frac{4}{-5}=-\frac{4}{5} \)

Answer:

\( \frac{7}{6} \)

Problem 2: (-5, 3) and (-1,0)