Q:

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. (4 points)Part B: Write the equation obtained in Part A using function notation.(2 points)Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Accepted Solution

A:
Answer:Here's what I get.Step-by-step explanation:Part A. Equation in standard formThe question is asking you to find the equation of a straight line that passes through two points Let x = the number of daysand y = the costThen the coordinates of the two points are (2,225) and (5,480).(i) Calculate the slope of the line[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\& = & \dfrac{480 - 225}{5 - 2}\\\\& = & \dfrac{255}{3}\\\\& = & 85\\\end{array}[/tex]In other words, the daily rental is $85/day.(ii) Calculate the y-intercept[tex]\begin{array}{rcl}y & = & mx + b\\480 & = & 85 \times 5 + b\\480 & = & 425 + b\\b & = & 55\\\end{array}[/tex](iii) Write the equation for the liney = 85x + 55That is, the cost is $55 Β plus $85/dayPart B. Equation in function notationReplace y with Ζ’(x)Ζ’(x) = 85x + 55Part C. GraphingLet's say you want to plot a graph of the rental cost for up to ten days.(i) Calculate two points on the graph.When x = 0, y = 85; when x = 10, y = 905.(ii) Scale your axesA good number of intervals is about ten.Your x-axis should have tick marks at 1-day intervals.Your largest y-value is 905. Ten intervals would make about $90/interval. However, you should round that up to $100/interval for easy interpolation.Your y-axis will run from 0 to $1000 in $100 intervals.Plot your two points and draw a straight line through them.(iii) Axis labelsx represents the number of days, so the label on the x-axis could be "No. of days."y represents the cost of renting the boat, so the label on the y-axis could be "Rental cost."Your graph should resemble the one below.