Since the problem stated the weight and price are in a linear relationship, we can use y=mx+b.
First, let's calculate our slope.
m = (4950-3700)/(0.75-0.5) = 5000
Now, let's solve for b.
3700 = 5000(0.5) + b
Simplify the right side of the equation.
3700 = 2500 + b
Subtract 2500 from both sides
1200 = b
Now our equation looks like this:
y = 5000x + 1200
Let's plug 2.5 in for x to solve for the diamond cost.
y = 5000(2.5) + 1200
Simplify the right side.
y = 13700
The average price of a 2.5 carat diamond is $13700
