Question

For the table below, determine the function rule, and find each of the missing y-values.

Function Rule: ?
x y
1 4
3 6
4 7
5 ?
7 10
10 ?

Answer 1

The answer is 8 and 13


y = ax + b
y = 4, x = 1 ⇒ 4 = a + b
y = 6, x = 3 ⇒ 6 = 3a + b

Solve the system of equation:
a + b = 4
3a + b = 6
______
b = 4 - a
3a + b = 6
______
3a + 4 - a = 6
2a + 4 = 6
2a = 6 - 4
2a = 2
a = 2/2 = 1
b = 4 - a = 4 - 1 = 3

So, the function rule is: y = x + 3

Thus, if x = 7, then y = 7 + 3 = 10
If x = 10, then y = 10 + 3 = 13


x y
1 4
3 6
4 7
5 8
7 10
10 13