Page 341 - Start Up Mathematics_8 (Non CCE)

Example 12: Draw a graph to represent the rela tionship
between the perimeter and the side x of Y
a square given as “Perimeter (P) = 4 × Side,
i.e., P = 4x” using the following table: 18
16 (4, 16)
Side of square 1 1.5 2 3 4 14
x (in cm) 12 (3, 12)
Perimeter P 4 6 8 12 16 10
(in cm) Perimeter P (in cm) 8 (2, 8)

Solution: To sketch the graph, take the side of square 6 (1.5, 6)
4
x (in cm) on the X-axis and the perimeter 2 (1, 4)
P (in cm) on the Y-axis as per the following
scale: 0 1 2 3 4 5 X
Scale: X-axis: 10 small divisions = 1 cm Side x (in cm)

Y-axis: 5 small divisions = 2 cm

Example 13: Draw a graph to represent the relation Y
between area of a square and the side x of
2
the square, i.e., Area of square (A) = (Side) . 18
fi A = x 2 16 (4, 16)

Use the table given below. 14
Side of 12
square x (in cm) 1 2 3 4 10 (3, 9)
2
Area (in cm ) 1 4 9 16 Area of square (in cm 2 ) 8
6
Solution: To sketch the graph, take the side of the 4 (2, 4)
square (in cm) on the X-axis and area of 2 (1, 1)
2
the square (in cm ) on the Y-axis using the 0 1 2 3 4 5 X
following scale: Side of square (in cm)
Scale:
X-axis: 10 small divisions = 1 cm

Y-axis: 5 small divisions = 2 cm 2

The graph of the side of a square and the area of a square is not a linear graph (i.e., not a straight line).

Example 14: A certain amount of water was heated Time (t) in minutes 0 2 4 8 9 10
and the temperature at different
intervals of time was observed as Temperature (T) in °C 10 30 50 90 100 100
shown in the table given alongside:

Draw a temperature–time graph from t = 0 minute to t = 15 minutes. Use this graph to answer
the following questions:
(a) What is the temperature of water at t = 7 minutes?

(b) What is the temperature after 12 minutes?
(c) After how many minutes is the temperature 70ºC?
(d) After how many minutes of heating, does the temperature remain constant?
Why is it so?

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