_______________________________________

MATH133 Unit 1 Individual Project 2 A
1) The following graph shows the depreciation for the corporate airplane from 2006
to 2009. The plane was purchased new in 2006; therefore, x = 0 represents the
year 2006.
X – axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5 years
Y – axis (vertical) = price in $ amounts from 24,000 to 240,000
a) List the coordinates of two points on the graph in (x, y) form. The numbers on
the horizontal axis are 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5.
(___, ___),(___, ___)
b) Find the slope (rate of depreciation) of this line:
Answer:
Show your work here:
c) Find the linear equation of this line in slope-intercept form.
Answer:
Show or explain your work here:
d) If the rate of depreciation continues at the present rate, what will be the plane’s
value in the year 2017? Show how to use the linear equation from part c) to
obtain your answer.
Answer:
Show or explain your work here:
e) If the trend continued, in how many years would the plane’s value be $48000?
Show how to use the linear equation from part c) to obtain your answer.
Answer:
Show or explain your work here:
2) Suppose that the width of a rectangle is 5 inches shorter than the length and that
the perimeter of the rectangle is 50 inches. The formula for the perimeter of a
rectangle is P=2L+2W.
a) Set up an equation for the perimeter involving only L, the length of the rectangle.
Answer:
b) Solve this linear equation algebraically to find the length of the rectangle. Find
the width as well.
Answer: Length ______, Width ______
Show your work here:
c) Using the same width as your answer from part b), find a new perimeter if the
new length is 4 less than three times the width.
Answer:
Explain your work here in one or two sentences:
3) A marketing group developing online ad space is offering two payment options:
Option 1: $210 set up fee plus $10/inch of the ad
Option 2: No set up fee but $25/inch of the ad
Let x = inches of the proposed ad, for example, x = 2 for a column ad that is 2
inches long.
a) Write a mathematical model representing the total ad cost, C, in terms of
x for the following:
Option 1: C=_________________
Option 2: C=_________________
b) How many inches of ad space would need to be purchased for option 1
to be less than option 2? Set up an inequality and show your work
algebraically using the information in part a).
Answer:
Show your work here:
c) Summarize your findings in a brief sentence.
Answer:
4) Graph the equations on separate graphs by completing the tables and plotting
the points. You may use Excel or another web-based graphing utility.
a) Complete the table using the given values of x and the equation y = -2x + 7.
Show your work.
x y
-1
0
2
4
b) Graph the equation here by plotting the points from your table. For help on
creating your graph in Excel and inserting graphs into a Word Doc please see the
tutorial in the Assignment List.
c) Complete the table using the given values of x and the equation 3x – y = 8. Show
your work.
x y
0
1
2
3
4
d) Graph the equation here by plotting the points from your table. For help on
creating your graph in Excel and inserting graphs into a Word Doc please see the
tutorial in the Assignment List.

To answer these questions, we will break down each question and explain how to arrive at the answer.

1) a) To find the coordinates of two points on the graph, we need to find the corresponding y-values for the given x-values. The x-values given are 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5. We can read off the y-values from the graph at these x-values.

b) To find the slope (rate of depreciation) of the line, we can use the formula:
slope = (change in y)/(change in x)
Choose any two points on the line and calculate the change in y and change in x. Then divide the change in y by the change in x to find the slope.

c) To find the linear equation of the line in slope-intercept form (y = mx + b), you will need the slope and the y-intercept. The slope can be determined from part b) and the y-intercept can be found by looking at the point where the line intersects the y-axis.

d) To find the plane's value in the year 2017, we need to substitute the x-value of 2017 into the linear equation found in part c) and solve for y.

e) To find the number of years it takes for the plane's value to be $48000, we need to substitute the value of $48000 for y in the linear equation found in part c) and solve for x.

2) a) To set up an equation for the perimeter of the rectangle involving only L (length), we can use the formula P = 2L + 2W, where W represents the width of the rectangle.

b) To solve the linear equation algebraically, we need to substitute the given value for the perimeter (50 inches) into the equation from part a) and solve for L. Then, we can calculate the width by substituting the length value into the equation W = L - 5.

c) To find a new perimeter using the same width as the answer from part b), we need to substitute the new length (4 less than three times the width) into the equation for the perimeter and solve for P.

3) a) To write a mathematical model representing the total ad cost, C, in terms of x for both options, we need to use the given information. For option 1, the cost is a set-up fee of $210 plus $10 per inch of the ad. For option 2, there is no set-up fee but it costs $25 per inch of the ad.

b) To find the number of inches of ad space needed for option 1 to be less than option 2, we need to set up an inequality using the mathematical models from part a) and solve for x.

c) To summarize the findings, you can write a brief sentence comparing the number of inches of ad space needed for the two options.

4) a) To complete the table using the given values of x and the equation y = -2x + 7, substitute the x-values into the equation and solve for y.

b) To graph the equation, plot the points from the completed table on a graph.

c) To complete the table using the given values of x and the equation 3x - y = 8, substitute the x-values into the equation and solve for y.

d) To graph the equation, plot the points from the completed table on a graph.