Question

1. (-19, -6), (15, 16)
2. (-18, -20), (-18, -15)

find the slope of each line, and the y-

Explanation:

Step1: Identify the formula for slope

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

Problem 13: Points \((-19, -6)\) and \((15, 16)\)

Step2: Substitute values into slope formula

Here, \( x_1=-19 \), \( y_1 = - 6 \), \( x_2=15 \), \( y_2 = 16 \).
So, \( m=\frac{16-(-6)}{15 - (-19)}=\frac{16 + 6}{15+19}=\frac{22}{34}=\frac{11}{17} \).

Problem 15: Points \((-18, -20)\) and \((-18, -15)\)

Step3: Substitute values into slope formula

Here, \( x_1=-18 \), \( y_1=-20 \), \( x_2 = - 18 \), \( y_2=-15 \).
So, \( m=\frac{-15-(-20)}{-18-(-18)}=\frac{-15 + 20}{-18 + 18}=\frac{5}{0} \), which is undefined (vertical line).

Answer:

• For the line through \((-19, -6)\) and \((15, 16)\), the slope is \(\frac{11}{17}\).
• For the line through \((-18, -20)\) and \((-18, -15)\), the slope is undefined.