Equations of horizontal and vertical lines

key notes:

What are Horizontal and Vertical Lines?

• Horizontal line: A line that runs left to right and is parallel to the x-axis.
• Vertical line: A line that runs up and down and is parallel to the y-axis.

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Equation of a Horizontal Line

• All points on a horizontal line have the same y-coordinate.
• Equation is:

y=k

where k is a constant (the y-value for all points on the line).

Example:
y=3 means the line passes through all points with y=3, like (0, 3), (4,3), (-2, 3).

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Equation of a Vertical Line

• All points on a vertical line have the same x-coordinate.
• Equation is:

x=h

where hhh is a constant (the x-value for all points on the line).

Example:
x=−2 means the line passes through all points with x=−2, like (-2, 0), (-2, 5), (-2, -3).

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Characteristics

Line Type	Equation	Slope	Intercepts
Horizontal line	y=k	Slope m=0	y-intercept = k no x-intercept (unless k=0
Vertical line	x=h	Slope is undefined	x-intercept = h, no y-intercept (unless h=0)

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Graphing Horizontal and Vertical Lines

• Horizontal line: Draw a straight line through y=k parallel to the x-axis.
• Vertical line: Draw a straight line through x=h parallel to the y-axis.

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Examples

• Write the equation of a horizontal line passing through (2, 5):

y=5

• Write the equation of a vertical line passing through (-3, 4):

x=−3

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Practice

Write the equation of:

1. A horizontal line through (6, -1)
2. A vertical line through (0, 3)
3. A horizontal line through (-4, 0)
4. A vertical line through (7, -5)

Learn with an example

Let’s Practice!