Question

find the slope of the line that passes through each pair of points.

1. a(1, 3), b(4, 7)
2. c(3, 5), d(2, 6)
3. e(4, 0), f(5, 5)

Explanation:

Problem 9: \( A(1, 3), B(4, 7) \)

Step 1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1 = 1,y_1 = 3,x_2 = 4,y_2 = 7 \).

Step 2: Substitute the values into the formula

\( m=\frac{7 - 3}{4 - 1}=\frac{4}{3} \)

Step 1: Recall the slope formula

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

Step 2: Substitute the values into the formula

\( m=\frac{6 - 5}{2 - 3}=\frac{1}{-1}=- 1 \)

Step 1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1 = 4,y_1 = 0,x_2 = 5,y_2 = 5 \).

Step 2: Substitute the values into the formula

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

Answer:

\( \frac{4}{3} \)

Problem 10: \( C(3, 5), D(2, 6) \)