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Question
Draw the graph obtained from the table below:
| X | a | 3 | - 5 | 5 | c | - 1 |
| Y | - 1 | 2 | b | 3 | 4 | 0 |
Use the graph to find the values of a, b and c. State a linear relation between the variables x and y.
Solution
The table is:
| X | a | 3 | - 5 | 5 | c | - 1 |
| Y | - 1 | 2 | b | 3 | 4 | 0 |
Plotting the points as shown in the above table,
we get the following required graph:
When y = - 1, then x = - 3
⇒ a = - 3
When x = - 5, then y = - 2
⇒ b = - 2
When y = 4, then x = 7
⇒ c = 7
Let y = px + q ....(1)
be a linear relation between x and y
Substitute x = - 3 and y = - 1 in the equation (1), we have,
-1 = - 3p + q ....(2)
Substitute x = - 5 and y = - 2 in the equation (1), we have,
-2 = - 5p + q ....(3)
Subtracting (3) from (2), we have,
1 = 2p
⇒ p = `(1)/(2)`
From (3), we have,
-2 = -5p + q
-2 = -5`(1/2)`+q
⇒ -4 = -5 + 2q
⇒ 2q = 5 - 4
⇒ 2q = 1
∴ q = `(1)/(2)`
Thus, the linear relation is
y = px + q
⇒ y = `(1)/(2) x + (1)/(2)`
⇒ y = `(x + 1)/(2)`
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