Thank you for the opportunity to help you with your question!

For part a.) Look at the points on the graph. Let the horizontal axis be t, and the vertical axis be c. So we have the points (0, 180), (1, 165), (2, 150), etc. These represent your coordinates for (t, c). Each t is increasing by 1, and the c is decreasing by 15 every time, so our dt is 1 and our dc is -15. The formula to show this would be dc = -15dt.

b.) The equation for cost would be c = -15t + 180.

c.) Basically, we are just rewriting the equation from part b by solving it for t. So we have, t = (c - 180) / ( - 15)

d.) dt = dc/(-15). We got this by rewriting the equation from part a and solving for dt.

Please let me know if you need any clarification, if you need more explanation on how to solve the equations, or anything that you still need help with. I'm always happy to answer your questions.