Forming equations of horizontal and vertical lines

Write the equation of a horizontal line (y equals a constant) or a vertical line (x equals a constant) through a given point, and describe the gradient of each.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Beta: Plotting co-ordinates, Ex 13.01, pgs 230 & 231
  • Beta: Drawing line from equation, Ex 13.02, pg 233
  • Beta: Gradients, Ex 13.03 to Ex 13.06, pgs 235 & 239
  • Beta: Intercept of lines, Ex 13.07 to Ex 13.08, pgs 240 & 241
  • Beta: Horizontal and vertical lines, Ex 13.09, pg 243
  • Beta: Applying straight-line rules, Ex 13.10, pgs 244 to 246
  • Dr Austin Maths - Equation of a Straight Line Revision Practice GridQuestions PDF · Answers

Terminology

  • horizontal line
  • vertical line

Task goals

  • Write the equation of a horizontal line ($y=$ constant) or a vertical line ($x=$ constant) through a given point.
  • Identify whether a given equation of the form $x=c$ or $y=c$ describes a horizontal or a vertical line.
  • Find the equation of a horizontal or vertical line from a set of coordinate points or a table where one coordinate stays fixed.
  • Describe a line as parallel to the $x$-axis or parallel to the $y$-axis through a given point.
  • State that a horizontal line has a gradient of $0$ and that a vertical line has an undefined gradient.
  • Write the equations of all four sides of a rectangle or square from its vertices, using horizontal and vertical line equations.
  • Explain why a vertical line such as $x=5$ cannot be written in the form $y=mx+c$, and compare the positions of lines like $y=-6$ and $x=-6$.

Teaching guidance

  • Students should know x=c, y=x form.
  • Better students should be able to describe the gradient properties of these lines.

Key skills

  • Horizontal lines
  • Vertical lines
  • Equations of lines
  • Linear graphs
  • Coordinates
  • Gradient
  • Intercepts
  • Equation of line

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included