Question

In exercises 9-12 the points represented by the table lie on a line. find the slope of the line

Answer 1

The slopes are:

`- Exercise 9: \( (1)/(2) \)\\- Exercise 10: 0\\- Exercise 11: -4/0`

To find the slope of a line, you can use the formula:

`\[ \text{Slope} (m) = \frac{\text{Change in } y}{\text{Change in } x} \]`

For each set of points, calculate the change in \( y \) and the change in \( x \), then use these values to find the slope.

**Exercise 9:**

`\text{Change in } x &= 3 - (-9) = 12 \\\\\text{Change in } y &= 4 - (-2) = 6 \\\\\text{Slope} &= (6)/(12) = (1)/(2)`

**Exercise 10:**

`\text{Change in } x &= 8 - (-1) = 9 \\\text{Change in } y &= -6 - (-6) = 0 \\\text{Slope} &= (0)/(9) = 0`

**Exercise 11:**

`\text{Change in } x &= 0 - 0 = 0 \\\text{Change in } y &= -4 - 0 = -4 \\`

`Slope = (-4)/(0)`

In Exercise 11, the slope is undefined because the change in \( x \) is zero, which results in division by zero. This indicates a vertical line.

So, the slopes are:

`- Exercise 9: \( (1)/(2) \)\\- Exercise 10: 0\\- Exercise 11: -4/0`