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Linear Graphs

We plot points on a graph and join them. If the graph so obtained is a straight line, we say that it
is a linear graph. A linear graph shows a linear relationship between two quantities, where one is
independent and other is dependent, i.e., the change in one quantity changes the other linearly.
Example 7: The values of x and the corresponding value of y are given below. Plot a graph. Is the
relationship between x and y linear?
x y

2 4
4 8
6 12
8 16

Solution: Let us plot and join the ordered pairs, namely (2, 4), (4, 8), (6, 12) and (8, 16) on the graph.

Y
20

16
(8, 16)
12
(6, 12)
y
8
(4, 8)
4 (2, 4)

X
O(0, 0) 2 4 6 8 10 12
x

The graph obtained is a straight line, which shows a linear relationship between x and y.
Example 8: (Quantity and Cost)
Draw the graph for the given table. Also write the suitable scales on the axes.

Number of Bananas 1 2 3 4 5

Cost (in `) 5 10 15 20 25
Solution: Y Scale

25 On x-axis, 1 unit = 1 banana
(5, 25)
20 On y-axis, 1 unit = `5
(4, 20)
15
(3, 15)
Cost (in `) 10 (2, 10) Think and Answer

5
(1, 5)
Cost and quantity depend on
X
O(0, 0) 1 2 3 4 5 6 each other. Which is the independent variable
Number of Bananas in this case?

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