Question

find the slope of the line through the pair of points. 19. (5, 0) and (-4, 2) 20. (6, -6) and (6, 2) 21. (12, 3) and (-7, -5) 16. slope (m) = y-intercept (b) = equation: 17. slope (m) = y-intercept (b) = equation: 18. slope y-intercept (b) = equation:

Explanation:

Step1: Recall slope formula

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

Step2: Solve for problem 19

For points \( (5, 0) \) and \( (-4, 2) \), let \( (x_1, y_1)=(5, 0) \), \( (x_2, y_2)=(-4, 2) \).
Substitute into the formula: \( m=\frac{2 - 0}{-4 - 5}=\frac{2}{-9}=-\frac{2}{9} \).

Step3: Solve for problem 20

For points \( (6, -6) \) and \( (6, 2) \), let \( (x_1, y_1)=(6, -6) \), \( (x_2, y_2)=(6, 2) \).
Substitute into the formula: \( m=\frac{2 - (-6)}{6 - 6}=\frac{8}{0} \), which is undefined (vertical line).

Step4: Solve for problem 21

For points \( (12, 3) \) and \( (-7, -5) \), let \( (x_1, y_1)=(12, 3) \), \( (x_2, y_2)=(-7, -5) \).
Substitute into the formula: \( m=\frac{-5 - 3}{-7 - 12}=\frac{-8}{-19}=\frac{8}{19} \).

Answer:

1. Slope \( = -\frac{2}{9} \)
2. Slope is undefined
3. Slope \( = \frac{8}{19} \)