<h2>
Answer: f(7) = 17 &
f(8) = 20</h2>
Step-by-step explanation:
We can use f(3) = 5 and f(4) = 8 to write points that we can turn into an equation, and then solve for f(7) and f(8).
f(3) = 5 can be written as (3 , 5)
f(4) = 8 can be written as (4 , 8)
The slope of this line using the slope (y₂ - y₁) ÷ (x₂ - x₁) = (8 - 5) ÷ (4 - 3)
= 3
The equation of the line can be written in the point-slope form (y - y₁) = m(x - x₁)); where (x₁ , y₁) = (3 , 5):
y - 5 = 3 (x - 3)
Now, f(7) occurs when x = 7
y - 5 = 3 (7 - 3)
y - 5 = 12
y = 17
<h3> ∴ f(7) = 17</h3>
Now, f(8) occurs when x = 8
y - 5 = 3 (8 -3)
y - 5 = 15
y = 20
<h3> ∴ f(8) = 20</h3>