What is the linear costs equation, marginal costs, and average costs per 100 units for the following information: 12 units costs $445 and 50 units costs $1585

For the linear total cost relationship, note that you're given two observations in an (x, y) ordered pair form: (units, total costs at such units).

From those two observations use the fact that for a linear, slope m = \frac{\Delta y}{\Delta x} .

The marginal cost function is simply the first derivative of the total cost function.

From the total cost function C(q) you derived first (q = quantity units), the average cost function is \frac{C(q)}{q}