Name: Terri Woodard

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Unit 1 Individual Project – A

Name: Terri Woodard

1)         Solve the following algebraically. Trial and error is not an appropriate method of solution.  You must show all your work.

a)         2x + 3 = 8

Solution:

2x = 8-3

2x = 5

(Long, 2006, p.22)

b)

Solution:

(Long, 2006, p.22)

c)

Solution :

(Long, 2006, p.22)

d)

Solution:

(Long, 2006, pp. 102-105)

2)       a)       Solve  for y

Solution :

b)      When graphed, this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?

Slope = –

Y-intercept = 3    (Ogden & Fogiel, 1996, p.37)

c)       Using your answer from part a, find the corresponding value of y when x = 16.

Solution:

3)       The following graph shows Bob’s salary from the year 2000 to the year 2003.  He was hired in the year 2000; therefore, x = 0 represents the year 2000.

a)       List the coordinates of two points on the graph in (x, y) form.

( 0, 30000),( 1, 32000)

b)       Find the slope of this line:

Solution:

To find the slope of a line use the equation:

Slope(m) = y2-y1

x2-x1             (Ogden & Fogiel, 1996, p.36)

Let two points in the line be: P1 (0, 30000), P2 (1, 32000)

Therefore:

x1= 0; x2= 1;   and y1 = 30000; y2 = 32000

Slope (m) = 32000- 30000

1-0

= 2000

1

= 2000

c)       Find the equation of this line in slope-intercept form.

Answer: y = 2000x + 30000

Solution:

Consider point (0, 30000)

Equation in slope-intercept form is:

y = mx + b   (Ogden & Fogiel, 1996, p.36)

where: m = 2000

b = 30000or (0, 30000) for y-intercept (Ogden & Fogiel, 1996, p.36)

y = 2000x + 30000

d)       If Bob’s salary trend continued, what would his salary be in the year 2005?

Answer: salary(y) in 2005 = 40000

Solution:

Since Bob’s salary increases in an amount of 2000 each year, then by the 5th year (2005) his salary would be:

Let x = number of years that Bob works

m = rise or increase of salary per year

b   = initial salary

y    = his salary in 2005

since equation of a straight line using slope-intercept form is :

y   = mx + b                     (Ogden & Fogiel, 1996, p.36)

y   = 2000 (5) + 30000

= 10000 + 30000

= 40000

4)       Suppose that the width of a rectangle is 5 inches shorter than the length and that the perimeter of the rectangle is 50.

a)       Set up an equation for the perimeter involving only L, the length of the rectangle.

Answer:  P = 4L – 10

Solution:

Let L = length of the rectangle in inches

L-5    = width of the rectangle in inches

P       = perimeter of the rectangle

According to Smith (2005, p.412),   the equation for the perimeter of a rectangle is     P = 2(Length + width)

Therefore, P = 2 ( L + L-5)

P = 2 ( 2L- 5)

P = 4L – 10

b)       Solve this equation algebraically to find the length of the rectangle. Find the width as well.

Answer:  Length   15 inches, Width   10 inches

Solution:

Given:

To find width :

Given : Width (W) = L-5

W = 15 -5

W = 10 inches

5)       A tennis club offers two payment options:

Option 1:  \$42 monthly fee plus \$5/hour for court rental

Option 2:  No monthly fee but \$8.50/hour for court rental.

Let x = hours per month of court rental time.

a)            Write a mathematical model representing the total monthly cost, C, in terms of x for the following:

Option 1: C= 42 + 5X

Option 2: C= 8.50X

b)            How many hours would you have to rent the court so the monthly cost of option 1 is less than option 2? Set up an inequality and show your work algebraically using the information in part a.

C1 < C2

42 + 5x < 8.50X

42 < 8.50x -5x

42 < 3.50x

or    x  > 12 hours           ( Long, 2006, p. 22)

This means that I have to rent the court for more than 12 hours in order for the monthly cost of option 1 to be less than option 2

6)            Plot the following points on the given rectangular coordinate system by clicking on the given dots and dragging them.

e grid.

Points to plot:

(-3, 2 )

(-2, 1)

(1, -2)

If you were to connect these points with a line, where would the y-intercept be located? Give the answer in (x, y) form.

References

Long, Lynette. (2006). Painless Algebra. Barron’s Educational Series.

Ogden, James R. and Max Fogiel. (1996).The Essentials of Algebra and Trigonometry. Research and Education Assn.

Smith, Karl J. (2005). Essentials of Trigonometry. Thomson  Brooks/Cole.

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