Equations of Horizontal and Vertical Lines Lesson Plan for 9th ... - Free Printable

Problem Analysis:

The task involves identifying and writing equations for horizontal and vertical lines based on their graphical representations. Let's break it down step by step.

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#### Part (a): Horizontal Line
1. Graph Description: The line is a horizontal line passing through the point \((3, 2)\).
2. Key Property of Horizontal Lines: A horizontal line has a constant \(y\)-coordinate for all points on the line. This means the equation of a horizontal line is of the form:
\[
y = \text{constant}
\]
3. Identify the Constant: Since the line passes through the point \((3, 2)\), the \(y\)-coordinate of this point is \(2\). Therefore, the equation of the line is:
\[
y = 2
\]

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#### Part (b): Vertical Line
1. Graph Description: The line is a vertical line passing through the point \((1, 5)\).
2. Key Property of Vertical Lines: A vertical line has a constant \(x\)-coordinate for all points on the line. This means the equation of a vertical line is of the form:
\[
x = \text{constant}
\]
3. Identify the Constant: Since the line passes through the point \((1, 5)\), the \(x\)-coordinate of this point is \(1\). Therefore, the equation of the line is:
\[
x = 1
\]

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Final Answers:

1. Equation of the horizontal line:
\[
\boxed{y = 2}
\]

2. Equation of the vertical line:
\[
\boxed{x = 1}
\]

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Explanation:

- Horizontal Lines: All points on a horizontal line have the same \(y\)-coordinate. Thus, the equation is simply \(y = \text{constant}\), where the constant is the \(y\)-coordinate of any point on the line.
- Vertical Lines: All points on a vertical line have the same \(x\)-coordinate. Thus, the equation is simply \(x = \text{constant}\), where the constant is the \(x\)-coordinate of any point on the line.

This approach ensures that the equations are derived directly from the properties of horizontal and vertical lines and the given points.