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What types of lines do the pair of equations x=c and y=c represent graphically?
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What types of lines do the pair of equations x=c and y=c represent gra...
The pair of equations x=c and y=c represent two lines that are parallel to the x-axis and y-axis, respectively. The equation x=c represents a vertical line that passes through the point (c, 0) on the coordinate plane and extends indefinitely in both the positive and negative y-directions. Similarly, the equation y=c represents a horizontal line that passes through the point (0, c) on the coordinate plane and extends indefinitely in both the positive and negative x-directions. These lines are called constant-value lines because the value of x or y remains the same along the entire length of the line.
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What types of lines do the pair of equations x=c and y=c represent gra...
Types of lines represented by x=c and y=c
- x=c represents a vertical line passing through the point where x=c on the x-axis.
- y=c represents a horizontal line passing through the point where y=c on the y-axis.
Vertical line x=c
A vertical line x=c is perpendicular to the x-axis and passes through the point where x=c on the x-axis. All points on the line have the same x-coordinate, which is c.
The graph of x=c is a straight line parallel to the y-axis.
For example, the equation x=3 represents a vertical line passing through the point (3,0) on the x-axis.
Horizontal line y=c
A horizontal line y=c is perpendicular to the y-axis and passes through the point where y=c on the y-axis. All points on the line have the same y-coordinate, which is c.
The graph of y=c is a straight line parallel to the x-axis.
For example, the equation y=2 represents a horizontal line passing through the point (0,2) on the y-axis.
Intersection of x=c and y=c
If we graph both lines x=c and y=c on the same coordinate plane, they will intersect at the point (c,c). This point lies on both lines since it satisfies both x=c and y=c.
Therefore, the intersection of x=c and y=c is a single point (c,c) on the coordinate plane.
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What types of lines do the pair of equations x=c and y=c represent graphically?
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What types of lines do the pair of equations x=c and y=c represent graphically? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What types of lines do the pair of equations x=c and y=c represent graphically? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What types of lines do the pair of equations x=c and y=c represent graphically?.
What types of lines do the pair of equations x=c and y=c represent graphically? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What types of lines do the pair of equations x=c and y=c represent graphically? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What types of lines do the pair of equations x=c and y=c represent graphically?.
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