**Determine the Slope of a Line** To find the slope of a line passing through two given points, use the formula: \[ \text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1} \] **Given points:** - (2, -4) - (10, -2) **Steps to Calculate the Slope:** 1. Label the given points: - Point 1: \( (x_1, y_1) = (2, -4) \) - Point 2: \( (x_2, y_2) = (10, -2) \) 2. Substitute these values into the slope formula: \[ m = \frac{-2 - (-4)}{10 - 2} \] 3. Simplify: \[ m = \frac{-2 + 4}{8} \] \[ m = \frac{2}{8} \] \[ m = \frac{1}{4} \] Thus, the slope of the line is \(\frac{1}{4}\). **Interactive Elements:** - **Input Box**: Enter the calculated slope. - **Buttons**: Likely used for interacting with the tool (e.g., submit, reset). When ready, click "Continue" to proceed to the next part of the exercise.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Determine the Slope of a Line**

To find the slope of a line passing through two given points, use the formula:

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

**Given points:**

- (2, -4)
- (10, -2)

**Steps to Calculate the Slope:**

1. Label the given points:
   - Point 1: \( (x_1, y_1) = (2, -4) \)
   - Point 2: \( (x_2, y_2) = (10, -2) \)

2. Substitute these values into the slope formula:

   \[ m = \frac{-2 - (-4)}{10 - 2} \]

3. Simplify:

   \[ m = \frac{-2 + 4}{8} \]

   \[ m = \frac{2}{8} \]

   \[ m = \frac{1}{4} \]

Thus, the slope of the line is \(\frac{1}{4}\).

**Interactive Elements:**

- **Input Box**: Enter the calculated slope.
- **Buttons**: Likely used for interacting with the tool (e.g., submit, reset).

When ready, click "Continue" to proceed to the next part of the exercise.
Transcribed Image Text:**Determine the Slope of a Line** To find the slope of a line passing through two given points, use the formula: \[ \text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1} \] **Given points:** - (2, -4) - (10, -2) **Steps to Calculate the Slope:** 1. Label the given points: - Point 1: \( (x_1, y_1) = (2, -4) \) - Point 2: \( (x_2, y_2) = (10, -2) \) 2. Substitute these values into the slope formula: \[ m = \frac{-2 - (-4)}{10 - 2} \] 3. Simplify: \[ m = \frac{-2 + 4}{8} \] \[ m = \frac{2}{8} \] \[ m = \frac{1}{4} \] Thus, the slope of the line is \(\frac{1}{4}\). **Interactive Elements:** - **Input Box**: Enter the calculated slope. - **Buttons**: Likely used for interacting with the tool (e.g., submit, reset). When ready, click "Continue" to proceed to the next part of the exercise.
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