The following observed values of x and y are thought to fulfil the law y=ax+b

Find the values of a and b.

x  1  2  -3  0  5

y  12  19  -16  5  40

The given values of x and y satisfies the law y = ax + b.

When x = 1, y = 12

∴ 12 = a × 1 + b

⇒ a + b = 12           ...(1)

When x = 2, y = 19

∴ 19 = a × 2 + b

⇒ 2a + b = 19          ...(2)

Solving (1) and (2), we have

When a = 7, we have

7 + b = 12                          (Using (1))

⇒ b = 12 – 7 = 5

Thus, the value of a and b are 7 and 5 respectively.