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Mathematics

Statement 1: The graph of 2x - 5 = 0 is a line parallel to y-axis.

Statement 2: When the equations of line are of the form x = ± k (a constant), the lines are parallel to y-axis.

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Graphical Solution

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Answer

Given,

⇒ 2x - 5 = 0

⇒ 2x = 5

⇒ x = 52\dfrac{5}{2}

This represents a vertical line (parallel to the y-axis) at a distance of 52\dfrac{5}{2} units.

This line is at a distance of 52\dfrac{5}{2} units to the right of the y-axis because the x-coordinate of every point on the line is 52\dfrac{5}{2}.

∴ Statement 1 is true.

For equations of the form x = ± k.

These represent vertical lines (parallel to the y-axis) because the value of x remains constant at k or -k for all values of y.

∴ Statement 2 is true.

∴ Both the statements are true.

Hence, option 1 is the correct option.

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