Class 9 Exam > Class 9 Questions > x = 0 is the equation ofa)x-axisb)a line para...
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x = 0 is the equation of
- a)x-axis
- b)a line parallel to x-axis
- c)y-axis
- d)a line parallel to y-axis
Correct answer is option 'C'. Can you explain this answer?
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x = 0 is the equation ofa)x-axisb)a line parallel to x-axisc)y-axisd)a...
Explanation:
The equation x = 0 is a linear equation in one variable x. It means that the value of x is always equal to zero. Let's see what this equation represents.
Equation of x-axis:
The x-axis is a horizontal line passing through the origin (0,0) in the Cartesian plane. Its equation is y = 0. The x-coordinate of any point on the x-axis is always zero. Therefore, the equation x = 0 cannot represent the x-axis.
Equation of a line parallel to x-axis:
A line parallel to the x-axis is a horizontal line that never intersects the x-axis. Its equation is of the form y = c, where c is a constant. The value of y is constant for all values of x. Therefore, the equation x = 0 cannot represent a line parallel to the x-axis.
Equation of y-axis:
The y-axis is a vertical line passing through the origin (0,0) in the Cartesian plane. Its equation is x = 0. The y-coordinate of any point on the y-axis is always zero. Therefore, the equation x = 0 represents the y-axis.
Equation of a line parallel to y-axis:
A line parallel to the y-axis is a vertical line that never intersects the y-axis. Its equation is of the form x = c, where c is a constant. The value of x is constant for all values of y. Therefore, the equation x = 0 represents a line parallel to the y-axis.
Therefore, the correct answer is option 'C', which is the y-axis.
The equation x = 0 is a linear equation in one variable x. It means that the value of x is always equal to zero. Let's see what this equation represents.
Equation of x-axis:
The x-axis is a horizontal line passing through the origin (0,0) in the Cartesian plane. Its equation is y = 0. The x-coordinate of any point on the x-axis is always zero. Therefore, the equation x = 0 cannot represent the x-axis.
Equation of a line parallel to x-axis:
A line parallel to the x-axis is a horizontal line that never intersects the x-axis. Its equation is of the form y = c, where c is a constant. The value of y is constant for all values of x. Therefore, the equation x = 0 cannot represent a line parallel to the x-axis.
Equation of y-axis:
The y-axis is a vertical line passing through the origin (0,0) in the Cartesian plane. Its equation is x = 0. The y-coordinate of any point on the y-axis is always zero. Therefore, the equation x = 0 represents the y-axis.
Equation of a line parallel to y-axis:
A line parallel to the y-axis is a vertical line that never intersects the y-axis. Its equation is of the form x = c, where c is a constant. The value of x is constant for all values of y. Therefore, the equation x = 0 represents a line parallel to the y-axis.
Therefore, the correct answer is option 'C', which is the y-axis.
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x = 0 is the equation ofa)x-axisb)a line parallel to x-axisc)y-axisd)a line parallel to y-axisCorrect answer is option 'C'. Can you explain this answer?
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