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Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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**Title: Graphing a Line Through Two Points**

**Objective:**
Learn how to graph a line that passes through given points and determine the equation of the line.

**Instructions:**
Graph the line that passes through the points \((-7, 0)\) and \((8, 0)\) and determine the equation of the line.

**Detailed Explanation:**

1. **Identify the Points:**
   - Point A: \((-7, 0)\)
   - Point B: \((8, 0)\)

2. **Plot the Points on the Graph:**
   - On a coordinate plane, point A is located 7 units to the left of the origin along the x-axis.
   - Point B is located 8 units to the right of the origin along the x-axis.

3. **Draw the Line:**
   - Connect Point A and Point B with a straight line. Since both points lie on the x-axis, the line itself will be on the x-axis.

4. **Determine the Equation of the Line:**
   - The line that passes through \((-7, 0)\) and \((8, 0)\) appears to be horizontal, coinciding with the x-axis. This implies a slope of 0, as there is no change in the y-coordinate between the two points.
   - The equation of a horizontal line is of the form: \(y = c\), where \(c\) is the y-coordinate for any point on the line. 
   - Since both points have a y-coordinate of 0, the equation of the line is \(y = 0\).

**Graph Explanation:**
The graph provided displays a coordinate plane with the x-axis and y-axis ranging from -10 to 10. Both points, \((-7, 0)\) and \((8, 0)\), are plotted precisely on the x-axis. The line connecting these points is horizontal and aligns perfectly with the x-axis, illustrating that \(y = 0\) for all \(x\)-values along this line.

**Conclusion:**
A line passing through the points \((-7, 0)\) and \((8, 0)\) has an equation of \(y = 0\), confirming that it is a horizontal line lying along the x-axis.
Transcribed Image Text:**Title: Graphing a Line Through Two Points** **Objective:** Learn how to graph a line that passes through given points and determine the equation of the line. **Instructions:** Graph the line that passes through the points \((-7, 0)\) and \((8, 0)\) and determine the equation of the line. **Detailed Explanation:** 1. **Identify the Points:** - Point A: \((-7, 0)\) - Point B: \((8, 0)\) 2. **Plot the Points on the Graph:** - On a coordinate plane, point A is located 7 units to the left of the origin along the x-axis. - Point B is located 8 units to the right of the origin along the x-axis. 3. **Draw the Line:** - Connect Point A and Point B with a straight line. Since both points lie on the x-axis, the line itself will be on the x-axis. 4. **Determine the Equation of the Line:** - The line that passes through \((-7, 0)\) and \((8, 0)\) appears to be horizontal, coinciding with the x-axis. This implies a slope of 0, as there is no change in the y-coordinate between the two points. - The equation of a horizontal line is of the form: \(y = c\), where \(c\) is the y-coordinate for any point on the line. - Since both points have a y-coordinate of 0, the equation of the line is \(y = 0\). **Graph Explanation:** The graph provided displays a coordinate plane with the x-axis and y-axis ranging from -10 to 10. Both points, \((-7, 0)\) and \((8, 0)\), are plotted precisely on the x-axis. The line connecting these points is horizontal and aligns perfectly with the x-axis, illustrating that \(y = 0\) for all \(x\)-values along this line. **Conclusion:** A line passing through the points \((-7, 0)\) and \((8, 0)\) has an equation of \(y = 0\), confirming that it is a horizontal line lying along the x-axis.
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