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A line parallel to the x-axis is a horizontal line. The equation of a horizontal line is of the form y = k, where k is the y-coordinate of any point on the line.

Mathematics

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4. Determine the equation of the line passing through the point (0,−1)(0, -1) and parallel to the x-axis.

  1. A line parallel to the x-axis is a horizontal line.

    The equation of a horizontal line is of the form y=ky = k, where kk is the y-coordinate of any point on the line.

  2. The line passes through (0,−1)(0, -1), so its y-coordinate is −1-1.

    The equation of the line is y=−1\boxed{y = -1}.
    The gradient of any horizontal line is 0\boxed{0}.

    5. Determine the equation of the line passing through the point (−1,0)(-1, 0) and parallel to the y-axis.

  3. A line parallel to the y-axis is a vertical line.

    The equation of a vertical line is of the form x=hx = h, where hh is the x-coordinate of any point on the line.

  4. The line passes through (−1,0)(-1, 0), so its x-coordinate is −1-1.

    The equation of the line is x=−1\boxed{x = -1}.
    The gradient of any vertical line is undefined\boxed{\text{undefined}}.

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