Unit 1-Linear Equations and Inequalities

0

MTH133

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 ,

.22

Solution (Long , 2006 ,

.22

Solution (Long , 2006 ,

.22

Solution (Long , 2006 , pp . 102-105

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 Y-intercept 3 (Ogden Fogiel , 1996 ,

.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

Answer : 2000

Solution

To find the slope of a line use the equation

Slope (m y2-y1

x2-x1 (Ogden Fogiel , 1996 ,

.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 ,

.36

where : m 2000

b 30000or (0 , 30000 ) for y-intercept (Ogden Fogiel 1996 ,

.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 br

.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 :

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 ,

.412 , the equation for the perimeter of a rectangle is

2 (Length width

Therefore ,

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 To find width

Given : Width (W L-5

W 15 -5

W 10 inches 5 ) A tennis club...