To fill in the missing information in the chart, let's analyze each point-slope equation given and extract the slope and a point on the line.
For the First Point-Slope Equation:
Equation: \( y - 6 = 3(x - 5) \)
- Identifying the slope and point:
- Slope \( m = 3 \)
- Point on line: \( (5, 6) \)
For the Second Point-Slope Equation:
Equation: \( y - 4 = -9(x + 8) \)
- Identifying the slope and point:
- Slope \( m = -9 \)
- Point on line: \( (-8, 4) \)
For the Third Point-Slope Equation:
Equation: \( y + 3 = 2(x - 5) \)
- Identifying the slope and point:
- Slope \( m = 2 \)
- Point on line: \( (5, -3) \)
For the Fourth Point-Slope Equation:
Equation: \( y - 4 = -10(x - 1) \)
- Identifying the slope and point:
- Slope \( m = -10 \)
- Point on line: \( (1, 4) \)
Compiled Answers:
Now we can fill in the missing information in the original chart:
| Point-Slope Equation | Slope | Point on line | |-------------------------|-------|---------------| | \( y - 6 = 3(x - 5) \) | 3 | \( (5, 6) \) | | \( y - 4 = -9(x + 8) \)| -9 | \( (-8, 4) \) | | \( y + 3 = 2(x - 5) \) | 2 | \( (5, -3) \) | | \( y - 4 = -10(x - 1) \)| -10 | \( (1, 4) \) |
Summary:
- For \( y - 6 = 3(x - 5) \): Slope = 3, Point = \( (5, 6) \)
- For \( y - 4 = -9(x + 8) \): Slope = -9, Point = \( (-8, 4) \)
- For \( y + 3 = 2(x - 5) \): Slope = 2, Point = \( (5, -3) \)
- For \( y - 4 = -10(x - 1) \): Slope = -10, Point = \( (1, 4) \)