Horizontal and Vertical Lines

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HORIZONTAL AND VERTICAL LINES

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The points ( x , y ) that satisfy the equation x = 3 are all points of the form ( 3 , y ) , where y can be any real number.
This is the vertical line that crosses the x-axis at 3.

The points ( x , y ) that satisfy the equation y = 3 are all points of the form ( x , 3 ) , where x can be any real number.
This is the horizontal line that crosses the y-axis at 3.

Equations of the form x = k graph as vertical lines.
The y-axis ( x = 0 ) is a vertical line.
Other vertical lines are parallel to the y-axis, and perpendicular to the x-axis.
Vertical lines have no slope; i.e., the slope is not defined.

Equations of the form y = k graph as horizontal lines.
The x-axis ( y = 0 ) is a horizontal line.
Other horizontal lines are parallel to the x-axis, and perpendicular to the y-axis.
Horizontal lines have slope 0 (zero).

EXAMPLES:
Question: Write the equation of the horizontal line that passes through the point (3,-2) .
Answer: y = -2

Question: Write the equation of the line through (3,-2) that is perpendicular to the x-axis.
Answer: x = 3

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