Linear Models Diamond problem

Question

Diamonds are priced by their carat weight. A 0.12 carat diamond is priced at $334.50 and a 0.17 carat weight diamond is priced at $1,629. Find an equation for the line that passes through these data points. If you were to use your equation to predict the price of a 0.17 carat diamond, would this be interpolation or extrapolation? All answers need to be rounded to exactly 2 decimal places because it represents money.

Equation of the line = y = Answer(x)-Answer

Is this interpolation or extrapolation

Answer 1

Use two-point form with (0.12, 334.50) and (0.17, 1629)

(y - 334.50) / (x - 0.12) = (1629 - 334.50) / (0.17 - 0.12)

(y - 334.50) / (x - 0.12) = 258900

y - 334.50 = 258900(x - 0.12)

y - 334.50 = 258900x - 31068

y = 258900x - 30733.5

Why would you need the predict the cost of a 0.17 carat? It is given as $1629.