**Slope Calculation for a Line Passing Through Two Points** To find the slope of the line passing through the points \((-8, -3)\) and \((-3, 4)\), follow these steps: 1. **Identify the Points:** - Point 1: \( (-8, -3) \) - Point 2: \( (-3, 4) \) 2. **Find the Change in Coordinates:** - Change in \( y \) (Δy) = \( y_2 - y_1 = 4 - (-3) = 4 + 3 = 7 \) - Change in \( x \) (Δx) = \( x_2 - x_1 = -3 - (-8) = -3 + 8 = 5 \) 3. **Calculate the Slope (m):** - Slope (m) = \( \frac{Δy}{Δx} = \frac{7}{5} \) The slope of the line is \( \frac{7}{5} \). **Graphical Representation:** The image contains the following elements related to finding the slope: - **Text Instructions:** "Find the slope of the line passing through the points (-8, -3) and (-3, 4)." - **Input Field:** A blank space for entering the calculated slope. - **Multiple Choice Options:** Several graphical icons representing different slope values, including an option labeled 'Undefined.' - **Buttons:** To continue to the next step after entering or selecting an answer. In this scenario, the slope should be entered as a fraction or selected if the correct option is available among the graphical choices. The user needs to ensure the slope \( \frac{7}{5} \) is correctly represented.
**Slope Calculation for a Line Passing Through Two Points** To find the slope of the line passing through the points \((-8, -3)\) and \((-3, 4)\), follow these steps: 1. **Identify the Points:** - Point 1: \( (-8, -3) \) - Point 2: \( (-3, 4) \) 2. **Find the Change in Coordinates:** - Change in \( y \) (Δy) = \( y_2 - y_1 = 4 - (-3) = 4 + 3 = 7 \) - Change in \( x \) (Δx) = \( x_2 - x_1 = -3 - (-8) = -3 + 8 = 5 \) 3. **Calculate the Slope (m):** - Slope (m) = \( \frac{Δy}{Δx} = \frac{7}{5} \) The slope of the line is \( \frac{7}{5} \). **Graphical Representation:** The image contains the following elements related to finding the slope: - **Text Instructions:** "Find the slope of the line passing through the points (-8, -3) and (-3, 4)." - **Input Field:** A blank space for entering the calculated slope. - **Multiple Choice Options:** Several graphical icons representing different slope values, including an option labeled 'Undefined.' - **Buttons:** To continue to the next step after entering or selecting an answer. In this scenario, the slope should be entered as a fraction or selected if the correct option is available among the graphical choices. The user needs to ensure the slope \( \frac{7}{5} \) is correctly represented.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:**Slope Calculation for a Line Passing Through Two Points**
To find the slope of the line passing through the points \((-8, -3)\) and \((-3, 4)\), follow these steps:
1. **Identify the Points:**
- Point 1: \( (-8, -3) \)
- Point 2: \( (-3, 4) \)
2. **Find the Change in Coordinates:**
- Change in \( y \) (Δy) = \( y_2 - y_1 = 4 - (-3) = 4 + 3 = 7 \)
- Change in \( x \) (Δx) = \( x_2 - x_1 = -3 - (-8) = -3 + 8 = 5 \)
3. **Calculate the Slope (m):**
- Slope (m) = \( \frac{Δy}{Δx} = \frac{7}{5} \)
The slope of the line is \( \frac{7}{5} \).
**Graphical Representation:**
The image contains the following elements related to finding the slope:
- **Text Instructions:** "Find the slope of the line passing through the points (-8, -3) and (-3, 4)."
- **Input Field:** A blank space for entering the calculated slope.
- **Multiple Choice Options:** Several graphical icons representing different slope values, including an option labeled 'Undefined.'
- **Buttons:** To continue to the next step after entering or selecting an answer.
In this scenario, the slope should be entered as a fraction or selected if the correct option is available among the graphical choices. The user needs to ensure the slope \( \frac{7}{5} \) is correctly represented.
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