Horizontal and vertical lines

Key points

A line is formed by coordinates with the same
\(y\)-coordinate (\(x\), \(y\)). This is generalised by the equation \(y = c\), where \(c\) is the constant \(y\)-coordinate.
A line is formed by coordinates with the same constant \(x\)-coordinate
(\(x\), \(y\)). This is generalised by the equation \(x = c\), where \(c\) is the constant \(x\)-coordinate.
The \(x\) is a horizontal line with equation \(y = 0\). The \(y\) is a vertical line with equation \(x = 0\)
A line is continuous and extends forever. It has an length. When drawing a shape, each side is a .

A horizontal line is made up of with a constant \(y\)-coordinate (\(c\)).The equation of the horizontal line is \(y = c\)

A vertical line is made up of coordinates with a constant \(x\)-coordinate (\(c\)).The equation of the vertical line is \(x = c\)

To draw the line \(y = c\):
1. Find the value \(c\) on the \(y\)-axis.
2. Draw a horizontal line through the coordinates (0, \(c\)).
3. Label the line with its equation.
To draw the line \(x = c\):
1. Find the constant value \(c\) on the \(x\)-axis.
2. Draw a vertical line through the coordinates (\(c\), 0).
3. Label the line with its equation.

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A horizontal line is made up of coordinates with a constant 𝒚-coordinate.
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Every coordinate on the line has a 𝒚-coordinate of 4. The constant is 4. The equation of the line is 𝒚 = 4
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Plot the line 𝒚 = 2
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Find the constant value (2) on the 𝒚-��澱��. Draw a horizontal line through the coordinates (0, 2). Label the line with its equation, 𝒚 = 2
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A vertical line is made up of coordinates with a constant 𝒙-coordinate.
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Every coordinate on the line has an 𝒙-coordinate of -5. The constant is -5. The equation of the line is 𝒙 = -5
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Plot the line 𝒙 = 7
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Find the constant value (7) on the 𝒙-��澱��. Draw a vertical line through the coordinates (7, 0). Label the line with its equation, 𝒙 = 7

Draw the line \(x = -4\)

The equation of the \(x\)-axis is \(y = 0\)

The equation of the \(y\)-axis is \(x = 0\)

To find the equation of a horizontal line, or line segment:
1. Extend the line to find the constant (\(c\)) at which it meets the \(y\)-axis.
2. Label the line with the equation \(y = c\)

For a line segment, state the values of \(x\) for which the line segment is drawn.

To find the equation of a vertical line, or line segment:
1. Extend the line to find the constant (\(c\)) at which it meets the \(x\)-axis.
2. Label the line with the equation \(x = c\)

For a line segment, state the values of \(y\) for which the line segment is drawn.

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Find the equations of each line segment that forms the rectangle.
Image caption,
The rectangle is drawn using two horizontal lines and two vertical lines.
Image caption,
Extend the vertical lines of the rectangle to meet the 𝒙-��澱��. One line meets the 𝒙-��澱�� at -8. The equation of the line is 𝒙 = -8. The line segment for this side of the rectangle is 𝒙 = -8 for values of 𝒚 from -3 to -7. The other line meets the 𝒙-��澱�� at 0. The equation of the line is 𝒙 = 0. The line segment for this side of the rectangle is 𝒙 = 0 for values of 𝒚 from -3 to -7
Image caption,
Extend the horizontal lines of the rectangle to meet the 𝒚-��澱�� (if needed). One line meets the 𝒚-��澱�� at -3. The equation of the line is 𝒚 = -3. The line segment for this side of the rectangle is 𝒚 = -3 for values of 𝒙 from -8 to 0. The other line meets the 𝒚-��澱�� at -7. The equation of the line is 𝒚 = -7. The line segment for this side of the rectangle is 𝒚 = -7 for values of 𝒙 from -8 to 0