Give the slope of the line passing through the each of the following pairs of points. Give your answers as integers or reduced fractions. If the line has no slope, enter DNE.

The line passing through (-3,-9) and (2,-9) has slope = 
   .

The line passing through (4,3) and (-7,-6) has slope = 
   .

The line passing through (2,6) and (-3,-4) has slope = 
   .

The line passing through (-6,2) and (-6,-7) has slope = 
   .

The line passing through (-1,5) and (2,-7) has slope = 
   .

To find the slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

### 1. The line passing through \((-3, -9)\) and \((2, -9)\)
\[
\text{slope} = \frac{-9 - (-9)}{2 - (-3)} = \frac{0}{5} = 0
\]

The slope is \(0\).

### 2. The line passing through \((4, 3)\) and \((-7, -6)\)
\[
\text{slope} = \frac{-6 - 3}{-7 - 4} = \frac{-9}{-11} = \frac{9}{11}
\]

The slope is \(\frac{9}{11}\).

### 3. The line passing through \((2, 6)\) and \((-3, -4)\)
\[
\text{slope} = \frac{-4 - 6}{-3 - 2} = \frac{-10}{-5} = 2
\]

The slope is \(2\).

### 4. The line passing through \((-6, 2)\) and \((-6, -7)\)
\[
\text{slope} = \frac{-7 - 2}{-6 - (-6)} = \frac{-9}{0}
\]

Since division by zero is undefined, the slope is **DNE** (the line is vertical).

### 5. The line passing through \((-1, 5)\) and \((2, -7)\)
\[
\text{slope} = \frac{-7 - 5}{2 - (-1)} = \frac{-12}{3} = -4
\]

The slope is \(-4\).

---

### Summary of slopes:

1. Slope of line through \((-3, -9)\) and \((2, -9)\) = \(0\)
2. Slope of line through \((4, 3)\) and \((-7, -6)\) = \(\frac{9}{11}\)
3. Slope of line through \((2, 6)\) and \((-3, -4)\) = \(2\)
4. Slope of line through \((-6, 2)\) and \((-6, -7)\) = **DNE**
5. Slope of line through \((-1, 5)\) and \((2, -7)\) = \(-4\)

Would you like any details or have further questions?

### Related questions:
1. How can you tell if a line is horizontal or vertical based on the slope?
2. How does a slope of 0 affect the appearance of a line?
3. How do undefined slopes differ from zero slopes?
4. What are the geometric implications of a slope being a fraction vs. an integer?
5. How do you find the equation of a line given a slope and a point?

### Tip: If the slope between two points is 0, the line is horizontal, meaning all \(y\)-values are the same.

Learn how to calculate the slope of lines passing through specific points such as (-3,-9) and (2,-9), using the slope formula. Understand different scenarios where slopes can be zero, undefined, or fractional. Suitable for students in Grades 7-10.

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