If a 8 oz cup of coffee is $2.10 and a 20 oz is $3.30, how much should a cup 10 oz and 16 oz cost?

Question

Linear interpolation

Answer 1

Assuming the relationship is linear:

The slope between (8, 2.10) and (20, 3.30), using the slope equation (y₂ - y₁)/(x₂ - x₁) is:

(3.3 - 2.1)/(20 - 8) = 1.2/12 = 0.1

So we can write the equation of the line using the point-slope form where m = 0.1 and (x₁, y₁) = (8, 2.1) as:

y - 2.1 = 0.1(x - 8)

y = 0.1x + 1.3

Now, to calculate the price of a 10 oz cup, plug in x = 10 or to calculate the price of a 16 oz cup, plug in x = 16.