Question

Fill in the missing information in the chart.
Point-Slope Equation
y- 6=3(x-5)
y -4=-9(x+8)
—====
Answer
-=_
Answer
_----
₫y+3=2(x-5)
# (-8,4)
::3

Slope
Point on line

Answer
Answer
!

I Answer 1-----:
Answer

-10
(1,4)
!
2
(5,-3)
-9
y - 4= -10(x-1)
$ (5,6)

Answer 1

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 = \( (1, 4) \)