Answer:
h(5) = - 22
Step-by-step 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)
