Answer:
Here's what I get.
Step-by-step explanation:
Part A. Equation in standard form
The question is asking you to find the equation of a straight line that passes through two points
Let x = the number of days
and y = the cost
Then the coordinates of the two points are (2,225) and (5,480).
(i) Calculate the slope of the line
![\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\& = & \dfrac{480 - 225}{5 - 2}\\\\& = & \dfrac{255}{3}\\\\& = & 85\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7Dm%20%26%20%3D%20%26%20%5Cdfrac%7By_%7B2%7D%20-%20y_%7B1%7D%7D%7Bx_%7B2%7D%20-%20x_%7B1%7D%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7B480%20-%20225%7D%7B5%20-%202%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7B255%7D%7B3%7D%5C%5C%5C%5C%26%20%3D%20%26%2085%5C%5C%5Cend%7Barray%7D)
In other words, the daily rental is $85/day.
(ii) Calculate the y-intercept
![\begin{array}{rcl}y & = & mx + b\\480 & = & 85 \times 5 + b\\480 & = & 425 + b\\b & = & 55\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7Dy%20%26%20%3D%20%26%20mx%20%2B%20b%5C%5C480%20%26%20%3D%20%26%2085%20%5Ctimes%205%20%2B%20b%5C%5C480%20%26%20%3D%20%26%20425%20%2B%20b%5C%5Cb%20%26%20%3D%20%26%2055%5C%5C%5Cend%7Barray%7D)
(iii) Write the equation for the line
y = 85x + 55
That is, the cost is $55 plus $85/day
Part B. Equation in function notation
Replace y with ƒ(x)
ƒ(x) = 85x + 55
Part C. Graphing
Let'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 axes
A 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 labels
x 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.