Special Cases — Horizontal and Vertical Lines Class 9 Maths | Introduction to Linear Polynomials

Understand it

In y = k, every point on the line has the same y-coordinate, so the line is parallel to the x-axis. In x = h, every point has the same x-coordinate, so the line is parallel to the y-axis. These special cases are important because one variable is fixed while the other can change.

Example

The graph of y = 3 passes through (0, 3), (2, 3), and (-4, 3). The graph of x = -2 passes through (-2, 0), (-2, 5), and (-2, -3).

Formula and rule

Horizontal line: y = k.

Vertical line: x = h.

Here k and h are constants.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Plot y = -2.

1Choose points (-3, -2), (0, -2), and (4, -2).
2Since all have the same y-coordinate, joining them gives a horizontal line.

Method you can reuse

Check which variable is fixed, list points by keeping that coordinate constant, plot at least two points, and draw the line parallel to the correct axis.

Sketch it in your answer

Draw y = k parallel to the x-axis and x = h parallel to the y-axis, marking two or three points on each line.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What type of line is x = 5 on the Cartesian plane?

Think first, then show answer

x = 5 is a vertical line because every point on it has x-coordinate 5 while y can take different values.

Common wrong answer

For x = 4, students may draw a horizontal line through 4 on the y-axis, but x = 4 must be vertical.

Exam tip

If y is constant, the line is horizontal. If x is constant, the line is vertical.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Students may be asked to identify the graph from the equation, write the equation of a horizontal or vertical line, or match points to the line.

1
Enough for 1 mark
Horizontal lines have equations of the form y = k, where y stays constant. Vertical lines have equations of the form x = h, where x stays constant.
2
Add for 2 marks
Example: The graph of y = 3 passes through (0, 3), (2, 3), and (-4, 3). The graph of x = -2 passes through (-2, 0), (-2, 5), and (-2, -3).
3
Add for 3 marks
In y = k, every point on the line has the same y-coordinate, so the line is parallel to the x-axis.

Use the concept graph around this idea instead of revising it in isolation.

Graphical Visualisation of Linear Polynomials

Graphical visualisation means representing the solutions of a linear equation in two variables as points on the Cartesian plane. These points lie on a straight line.

Linear Polynomial in Two Variables

A linear polynomial or linear equation in two variables has the form ax + by + c = 0, where x and y are variables, a, b, and c are constants, and a and b are not both zero.

Polynomial — Definition and Degree

A polynomial is an algebraic expression made using variables, constants, coefficients, and non-negative whole number powers of variables. The degree is the highest power of the variable present in the polynomial.

Linear Polynomial in One Variable

A linear polynomial in one variable is a polynomial of degree 1, usually written as ax + b, where a and b are constants and a is not equal to 0.

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Special Cases — Horizontal and Vertical Lines

Understand it

See it worked out

Check yourself

Write it in the exam

Practice this concept with focused MCQs

Help improve this page

Special Cases — Horizontal and Vertical Lines

Understand it

See it worked out

Check yourself

Write it in the exam

Related concepts

Practice this concept with focused MCQs

Help improve this page