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

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)