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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.

In one line: Equation gives many points; graph joins them into one straight line.

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Understand it

To draw the graph of a linear equation, choose convenient values of one variable, find the corresponding values of the other variable, make ordered pairs, and plot them. Joining the points gives a straight line. Every point on the line represents a solution of the equation.

Example

For x + y = 5, points such as (0, 5), (2, 3), and (5, 0) lie on the same straight line.

Formula and rule

For ax + by = c, each solution (x, y) is a point on its straight-line graph.

See it worked out

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

Worked example

Graph 2x + y = 6.

  1. 1If x = 0, y = 6, giving (0, 6).
  2. 2If x = 3, y = 0, giving (3, 0).
  3. 3Plot these two points and join them to get the straight line.

Method you can reuse

Rewrite if needed, choose easy x-values, calculate y-values, form ordered pairs, select a suitable scale, plot points, join them, and label the graph.

Sketch it in your answer

Draw x-axis and y-axis with equal scale, prepare a value table, plot at least two points, join with a ruler, and label the line.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why do the points (0, 4), (2, 2), and (4, 0) lie on the graph of x + y = 4?

Think first, then show answer
They lie on the graph because each ordered pair satisfies x + y = 4, and all such solutions form one straight line.

Common wrong answer

For 2x + y = 6, students may plot (6, 0) instead of (0, 6) by swapping the intercept coordinates.

Don't mix this up

Students sometimes plot (x, y) as (y, x), which places the point in the wrong position.

Exam tip

Use at least two correct points to draw a straight line, and label axes, scale, points, and the equation of the line.

Graphical Visualisation of Linear Polynomials diagram

Open full screen to read every label clearly.

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

Questions may ask students to complete a table, plot the graph, identify whether a point lies on a line, or read intercepts from a graph.
  1. 1

    Enough for 1 mark

    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.

  2. 2

    Add for 2 marks

    Example: For x + y = 5, points such as (0, 5), (2, 3), and (5, 0) lie on the same straight line.

  3. 3

    Add for 3 marks

    To draw the graph of a linear equation, choose convenient values of one variable, find the corresponding values of the other variable, make ordered pairs, and plot them.

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