equation of line parallel to y axis
Understand the Problem
The question is asking for the equation of a line that runs parallel to the y-axis. Such a line will have the same x-coordinate for all points on it, typically expressed in the form x = a, where a is a constant.
Answer
The equation of the line is \( x = a \).
Answer for screen readers
The equation of the line parallel to the y-axis is ( x = a ), where ( a ) is the specific x-coordinate.
Steps to Solve
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Identify the x-coordinate Determine the specific x-coordinate for the line that is parallel to the y-axis. For example, if you want the line to pass through the point (a, b), the x-coordinate is ( a ).
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Formulate the equation The equation of a line parallel to the y-axis can be expressed simply as ( x = a ). This means that at every point on this line, the x-value remains constant.
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Example equation If the line is to pass through the point (3, 5), the equation would be:
$$ x = 3 $$
This indicates that the line is vertical and all points on the line will have an x-coordinate of 3.
The equation of the line parallel to the y-axis is ( x = a ), where ( a ) is the specific x-coordinate.
More Information
A vertical line (one that runs parallel to the y-axis) has an undefined slope, while all points on this line have the same x-value. For example, the line ( x = 4 ) runs through all points where x is equal to 4, regardless of the y-coordinate.
Tips
- Confusing lines parallel to the y-axis with horizontal lines: A horizontal line has a fixed y-coordinate and is expressed as ( y = b ), while a vertical line has a fixed x-coordinate.
- Forgetting to specify the value of ( a ): Always provide the constant value for the x-coordinate in the line’s equation.
