Question

If h is a linear function with h(1) = 10 and h(3) = -6, what is h(5)?

Answer 1

h(5) = - 22

Explanation:

Given that h is a linear function say, h(x) = ax + b ......... (1)

Now, given that h(1) = 10 and h(3) = - 6

Hence, we can write from equation (1), a(1) + b = 10, ⇒ a + b = 10 .......... (2)

And a(3) + b = - 6, ⇒ 3a + b = - 6 ........ (3)

Now, solving equations (2) and (3) we get (3a - a) = - 6 - 10

⇒ 2a = - 16

⇒ a = - 8

So, from equation (2), we get, b = 10 - a = 18

Therefore, the linear function is

h(x) = - 8x + 18

Hence, h(5) = - 8(5) + 18 = - 22 (Answer)