Question

Use the table given below to draw the graph.

X	- 5	- 1	3	b	13
Y	- 2	a	2	5	7

From your graph, find the values of 'a' and 'b'.
State a linear relationship between the variables x and y.

Answer 1

The table is:

X	- 5	- 1	3	b	13
Y	- 2	a	2	5	7

Plotting the points as shown in the above table, we get the following required graph:

When x = - 1, then y = 0
⇒ a = 0
When y = 5, then x = 9
⇒  b = 9

Let y = px + q                   ....(1)
be a linear relation between x and y

Substitute x = 9 and y = 5 in the equation (1), we have,
5 = 9p + q                          ....(2)

Substitute x = - 1 and y = 0 in the equation (1), we have,
0 = - p + q                          ....(3)

Subtracting (3) from (2), we have,
5 = 10p

⇒ p = `(5)/(10)`

⇒ p = `(1)/(2)`

From (3), we have,
p = q

∴ q = `(1)/(2)`

Thus, the linear relation is

y = px + q

⇒ y = `(1)/(2) x+(1)/(2)`

⇒ y = `(x + 1)/(2)`