Answer:
a = 1
b = 5
⇒ f(x) = x + 5
Step-by-step explanation:
Given
- f(x) = ax + b
- f(1) = 6
- f(-2) = 3
Therefore,
f(1) = 6 ⇒ a + b = 6
f(-2) = 3 ⇒ -2a + b = 3
Rewrite a + b = 6 to make a the subject, substitute into -2a + b = 3 and solve for b:
a = 6 - b
⇒ -2(6 - b) + b = 3
⇒ -12 + 2b + b = 3
⇒ -12 + 3b = 3
⇒ 3b = 15
⇒ b = 5
Substitute found value for b into a + b = 6 and solve for a:
⇒ a + 5 = 6
⇒ a = 1
Therefore, f(x) = x + 5
