SOLUTION: Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480. Write an equation in the standard form to represent the tot

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Question 1018101: Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480. Write an equation in the standard
form to represent the total rent (y) that Sam has to pay for renting the boat for x days.
Part B: Write the equation obtained in Part A using function notation.
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The two points you are given are and .

Part A: Use the two-point form to derive an equation for the line that passes through your two points.

where and are the coordinates of the given points.

Rearrange this equation into standard form, namely: Note: Some instructors demand that and be integers and that be non-negative.

Part B: Solve the equation of part A for in terms of everything else, so that you have the slope-intercept form . Then replace with

Part C: The easiest way is to plot the two points given at the start of the discussion and draw a straight line through them. Use a reasonable interval for the domain of your function. Ask yourself questions like, "is it reasonable that Sam would rent the boat for a negative number of days?" or "would Sam be likely to pay a rental fee that would be in excess of what purchase price of the boat would be?" (to get an idea of the maximum number of days he might rent the boat). You might want to specify that the function is defined over the integers. While it is possible that the owner of the boat might have a granularity of half-days, he certainly wouldn't rent it for say, the square root of 2 days.

John

My calculator said it, I believe it, that settles it