Page 45 - Mathematics Class - XI

ACTIVITY 5.2

OBJECTIVE
To verify that the graph of a given inequality, say 5x + 4y – 40 < 0, of the form ax + by + c < 0, a, b > 0 and
c < 0 represents only one of the two half planes.

MATERIAL REQUIRED
 Cardboard  Graph paper  Ruler
 White chart paper  Sketch pen  Glue

PRE-REQUISITE KNOWLEDGE
1. Knowledge of linear equations in one variable and two variables

2. Knowledge of inequation and sign of inequality
3. Knowledge of making a graph of linear equation in two variables

PROCEDURE
1. Take a cardboard of a convenient size and paste a white chart paper on it.
2. Paste a graph paper on the white chart paper.
3. On the graph paper, draw two perpendicular lines X′OX and YOY′ to represent x-axis and y-axis,
respectively.

4. Find the ordered pairs of the form (x, y) which
satisfy the given equation 5x + 4y – 40 = 0,
corresponding to the given inequality.

A B C

x 0 4 8

y 10 5 0

5. Plot the points A (0, 10), B (4, 5) and C (8, 0) on
the graph as shown in Fig. (a).
6. On the graph, mark the two half planes as I and II
as shown in Fig. (a).

Fig. (a)
DEMONSTRATION
1. Mark some points O (0, 0), D (1, 2), E (3, 2), F (4, 3), G (–2, –2) in half plane I and points H (5, 7), I (7, 5),
J (8, 4), K (9, 5) in half plane II, as shown in Fig. (b).
2. Put these coordinates in the left hand side of the inequality 5x + 4y – 40 < 0 to verify.
(i) For point O (0, 0),
Value of LHS = 5(0) + 4(0) – 40 = – 40 < 0

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