Horizontal/vertical lines | Year 8

01 / LEARN

The idea, step by step

Horizontal lines fix the height

Every point on $y = 3$ has second coordinate 3 while its first coordinate can vary. Points such as $(- 2, 3), (0, 3), (4, 3)$ form a horizontal line.

This is not merely the point $(0, 3)$ . It contains all allowed x-values at the stated height.

Vertical lines fix horizontal position

Every point on $x = - 2$ has first coordinate -2 while its second coordinate can vary. The resulting line extends vertically. It cannot be represented by a single y-output for every x-input.

The coordinate axes are special cases: $y = 0$ is the x-axis and $x = 0$ is the y-axis.

A common trap

Calling x = 3 horizontal because x is the horizontal coordinate.

Instead: It fixes horizontal position, so the line extends vertically.

02 / WORKED EXAMPLES

See the thinking

Example 1

A horizontal line

Give three points on $y = - 2$ .

Keep the second coordinate -2.
Choose three different first coordinates.
The graph is horizontal.

For example

(- 3, - 2), (0, - 2), (4, - 2)

Example 2

A fixed first coordinate

A line contains $(3, - 1), (3, 0), (3, 4)$ . What is its equation?

All first coordinates equal 3.
The second coordinates vary.
The line is vertical, 3 units right of the y-axis.

x = 3

Check your understanding

Give the equation of the x-axis.

Show answer

$y = 0$ .

Every point there has second coordinate zero.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Give two points on $y = 4$ .
2 marks
Give two points on $x = - 1$ .
2 marks
Which line is vertical: $x = 5$ or $y = 5$ ?
2 marks
A horizontal line passes through $(4, - 3)$ . Give its equation.
2 marks
A vertical line passes through $(- 4, 2)$ . Give its equation.
2 marks
Where do $x = 2$ and $y = - 3$ intersect?
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Give two points on $y = 4$ .
2 marks
Keep y equal to 4.
Choose different x-values.
For example $(0, 4), (2, 4)$ .
Give two points on $x = - 1$ .
2 marks
Keep x equal to -1.
Choose different y-values.
For example $(- 1, 0), (- 1, 3)$ .
Which line is vertical: $x = 5$ or $y = 5$ ?
2 marks
It fixes horizontal position.
Its y-values vary.
$x = 5$ .
A horizontal line passes through $(4, - 3)$ . Give its equation.
2 marks
Use the point's constant y-coordinate.
The x-coordinate may vary.
$y = - 3$ .
A vertical line passes through $(- 4, 2)$ . Give its equation.
2 marks
Use the point's constant x-coordinate.
The y-coordinate may vary.
$x = - 4$ .
Where do $x = 2$ and $y = - 3$ intersect?
2 marks
The point must satisfy both equations.
Combine x = 2 and y = -3.
$(2, - 3)$ .

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics (2026)

Multi-step equations; brackets and variables on both sides; equations with rational solutions; substitution checks; one-variable inequalities and number-line solutions; tables and straight-line graphs; horizontal/vertical lines; how coefficients change a graph; graphical solutions and intersection checks; real-world linear models with digital exploration.

Official curriculum source ↗

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