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.

Answer 1

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)`