Forming equations of horizontal and vertical lines

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)

New NZC (2026)

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
CorbettMaths - x = a and y = a graphsQuestions PDF · Answers

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 $x=-6$.