Differentiate the given solution:

Substitute
and
into the ODE:

and it's easy to see the left side indeed reduces to 0.
Answer:
it should be A but im not fully sure
Original:350 discount:87.50 off new price: 262.5
As you increase the subintervals the area will be closer and closer to the real value. In other words your approximation gets better.
As you increase the intervals, there will be more rectanagles and the added area of these rectangles are converging towards the actual area under the curve.
Do you want the equation of the line given the slope and a point it goes through?
y - y1 = m (x - x1)
y - 16.5 = 1.75 (x - 10)
y - 16.5 = 1.75x -17.5
y = 1.75x - 1