unit 1: linear equation s - wikispacesunit+1-+linear... · f x (6) x - 3y = 8, with a y ... write...

Intermediate Algebra

Unit 1: Linear Equations

Graphing With Ordered Pairs:


Use the accompanying graph grid to answer the following questions:

State the coordinates of the indicated point: 3E rf- -i

i n

y / 1 f i| 9

i 1 f

i \ i k 9 f

i 1 §

(\ It i 1 V V w

A i m Name the lettered each ordered pair:

(7) (-2,6) E

(8) (0,-3) ^

(9) (5,-5)

(10) (-1,-1) ^

(11) (-7,-8) ^

(12) (7,-1) J

(1) A

(2) I

(3) H

(4) C

(5) E

(6) N

^ 5

(13) Where the x- and y-coordinates are equal

(14) Where the y-coordinate is three times the value of the x-coordinate

Name the quadrant or the axis on which each point lies:

(15) (-4,3) ^

(16) (0,6) .

(17) (4,-2) .

(18) (-1,-1) .

(19) (-2,0) .

(20) (1,2) ,

I E

i n

2

S!2Ee: ^,s^ ^ ^ ^

rn =

\>

3 m x -vV) V ^ *

Cwor/c space for next page)

3

<—>

1.

In Exercises 1-6, find the slope of AB.

2. y y

\ \ \

\ X

\ —V ?\

\

3.

X

A B

m

answers 1-6

^ 3

' 3

b . A 3 5

4. A f

X

B r

5.

7:1

6.

c X

z

12 ' 2

' 5

In Exercises 7-18, find the slope of the line that passes through the two given points.

7. (5,1); (8,3)

9 . (2. - 2 ) ; (5 .7)

n . ( - 3 . 7 ) ; ( -10.0)

^3- ( 0 . - 3 ) : ( - 2 . 7 )

15. ( - a 4 ) : ' ( 6 , - 5 )

17. ( -2 .11); (7.15)

8. f. (6 ,3) : (1,4)

10. (1, - 6 ) ; ( 9 , - 8 )

12. ( - 9 . 4 ) ; ( - 6 , - 4 )

14. (2,8): (0,3)

16. ( - 5 . - 9 ) ; (-1. -1)

18. ( - 5 . 6 ) ; (0.0)

a b

A c

111 — d e f g h i J k 1 m b

A T u 6 u Linear Equations and Their Graphs: Rnding Slope Given Two Points On the Line (Not Using the Graph) 4

PUNCHLINE . Algebra • Book A ©2006 Marcy Mathworks

Writing & Graphing Linear Equations:


3

(work space for next page)

plot OL+ t^JMit ^rftx po.ViH 4̂ LlvWl uii-A^ Or^'^\voJ <^x-b"ow

5

2 12 4 11 7 12 4 11 6 2

9 5 11 4 12 • 5 11 & 1 12 3 10 7

Vi. (3,1). (9 ,5 )

^ z j ^ t - 3

S 2 . (1,1), ( - 2 . 7)

Ai)S\^crs 1-6:

\. ( - 4 . - 3 ) , (8 ,0) - 3 - , ^ - . ) ^ b ^ j . ^ © y = - | x - 4 ( ^ O y =

ft 4. ( - 1 ,4 ) , ( - 4 , - 5 ) ^ ^ -3̂ /, ^ ̂ O y = ^

o5. (0, - 4 ) . ( - 4 , 6 ) ^ ^ - C M . t ^ . ' f , ^ I © y = 1 ^ - 1

•6. ( - 6 . 3 ) , (6, -1) I J' ' ' '3x ^ / © ^ ^ ^ 1

o y ^ 1 ^ 7

2© y = - 2 x + 3

G O y = 4 ^ + 1

y = 3a: + 7

©

3 0 y = | x - 2

(

e 7 . ( - 1 , - 6 ) . ( - 3 , - 8 ) Aos^^crs 7-12:

C8. ( - 1 ,3 ) . (3, 5)

3^/ '=5

X + ^

^ 9 . ( - 2 , 5). ( 1 , -7 )

i i p . ( i 2 ) . ( - f , 4 )

I t . ( l .3 )r ( -7 . -3) i - l ^ t

"8

S © y = + I

12. ( - 3 . 8 1 ( 0 . 0 ) 1,^0 J - - ' f x

® y p .

/ o ® y =

/ z © y =

® y > - - ^ ^

l © y = a: - 5

® y ^

Linear Equations and Their Graphs: Finding the Equation of a Line Given Two Points On the Line

PUNCHLINE • Algebra • Book A ©2006 Marcy Mathworks

Graphing Using Slope-Intercept Form:

Unit 1: Linear Equations : ?,

(1) y = 2 x - 4

/ J f 1

/ 1 1 r —

}

f }

f i 1 J

( J

(3) 3 x - y = 7

—1 • --

r -

-i-t--

i:

-4 si; '-\[

"i h

~ i ' -4^

2

(2) y = - | x + i _ _ 3-,

b - 1

(4) 2x + 3y = 6

s

•••••••••II^^EKIffE|)»?B

(5) x - 4 y + 8 = 0 —, ij + 2- V

-a

V I r •

(6) 6 x - 5 y = 1 5

o X

.4

7

2"

Parallel Lines: viCAêr iM+VîtL-t


Perpendicular Lines: r-\^<t. av-ês

1 no =̂

For questions (1) - (6), write an equation in slope-intercept form that passes through the given point and is P A R A L L E L to the graph of the given equation:

(1) y = -2x + 5 (3,1) (2) y = 3 x - 5 (-1,-2)

(3) y = | x + 5 (12,3) (4) y = - 7 X + ^ (4,-2) 4 4

b - 1

(5) 5 x - 4 y = 1 (-8,2)

~ i o + b

f x

(6) X - 3y = 8, with a y-intercept of -6

J

8

For questions (7) - (12), write an equation in slope-intercept form that passes through the given point and is PERPENDICULAR to the graph of the given equation:

(7) V = ^x-4 (-2,3) 4 (8) y4^4 (2,4)

)i4>

0

(9) y = 2x + 5 (-2,9) ( 1 0 ) 4 x + 3y = -6 (2,1)

( 1 1 ) x = 2 y - 1 (0,0)

J

(12) 5x - 3y = 2, with an x-intercept of 3

P a r a l l e l & P e r p e n d i c u l a r L i n e s :

Write a linear equation in slope-intercept form that passes through:

2 (1) the point (4, 6) and is parallel to the line y = - x + 5

3

n o - 5 6> -

3 ^ lo 3

3

(2) the point (2, -5) and is perpendicular to the line y = — x + 7 4

- S - - - % +b t J

"I (3) the point (-5, 6) and is perpendicular to the line 3x - - y = 3

5

^ 3

10

Writing Linear Equations: rr) b

(1) Write an equation of a line whose slope is -YA and y-intercept is -5.


(2) Write an equation of a line whose y-intercept is 1 and slope is - 1 . '

5- - I v + I (3) Write an equation of a line whose slope is zero and y-intercept is

- (o

(4) Which of the following lines isjoara//e/ to the line whose equation is 3y = 4x + 8?

3 / . r 7 4

es ispara

( 1 ) y = ^ 5 (2)y=X'+8 (3) 1̂ 4) y = ^ x - 5

(5) Which of the following lines is perpendicular to the line whose equation isjBx + 7y = 14?

(1) 7y (2) y = ;^x + 9 D

(3) 7 x > e f ^ 1 4 (4) ^12>tJ-44y^ 28

(6) Write an equation of a line whose slope is Yi and passes through the point (-4, 1).

(7) Write an equation of a line whose slope is -Ys and passes through the point (-3, 7).

i - a A-b

11

(8) Write an equation of a line that is perpendicular io the line y = V x̂ - 4 and passes through the point (4, 6). - 3. + b

(9) Write an equation of a line that is parallel io the line y = V2X + 5 and passes through the point (-10,1). , ,

b - 6>

Write an equation of a line that is perpendicular to the line 3x + 4y = 0 and passes through the point (-3, 7). , ^ ^ -

- 3

3

7 ^ - 1 + - b

Write an equation of a line that is perpendicular to the line 5y = through the point (4, 3). ^ ia ~

-2x + 10 and passes

5~

(12) Write an equation of a line that is parallel to the line 3y = 2x + 7 and passes through the point (-3,5). 4 ^ -7

-+-b

6 - 7 J 5 X + 1

Write an equation of a line that is parallel to the line 5x + 4y = 16 and passes through the point (1,2).

r ^ V ^ - r

-1 12

(14) Write an equation of a line that passes through the points (5, -4) and (2, 2).

no

<:R- ^ b

(15) Write an equation of a line that passes through the points (-2, 5) and (1 , 3).

3 - - S ( « U b

- -2-

3 ^ ' I + b

h - ^

3 >̂ 3

(16) Write an equation of a line that passes through the points (3, 2) and (6, 3).

3 -

5

© 3 - V b

13

X- and Y-lntercepts: a r e ^o.vxts cCiVve^ ' ^ r c ^ iVx^erSec+s •-o>^ ^^cix;j

Find the x- and y-intercepts for each linear equation:

(1)

x-intercept:

y-intercept:

(2)

j

1 1 : 5 ... - ' -i 1 -

I i i

x-intercept:

y-intercept:

x-intercept:

y-intercept: " " " ^

(4) Given the equation 2x + 3y = 6, find the x- and y-intercepts: 2-, 3

(a) graphically

S i

V ( 1 )

s

(b) algebraically

OClUvf uoW«rt^ " ^ ^ ^

14

(5)

x-intercept:

y-intercept:

(6)

(8)

Y /- - 0

x-intercept: ^ ' t>

y-intercept: ^ « ^

x-intercept:

y-intercept:

(9)

x-intercept: rJorJ£

y-intercept: 1

(7)


y

X-intercept:

y-intercept:

(10)

x-intercept: Si

y-intercept: A / p / v / e

State and use the x- and y-intercepts to graph each linear equation:

(12) x - 4 y = 4 (11) 3x + 2y = -6 V

(13) y = 0 . 5 x - 1

•

r A

r

V )

(14) y,x + y = 1

3 X ^

15

the x- and y-intercepts for each linear equation:


(15) 3x + 4 y = 1 2 (16) 2 x - 2 y = -4

(-1,0) (o^t.^

(17) 5 x - 3 y = 1 5

(18) y = 4x + 2

4 v -

(19) y = - 3 x - 9

3 x -l-y - S

(20) 4 x - 2 y - 8 = 0

state and use the x- and y-intercepts to graph each linear equation:

I (21) 6x + 3y = -18 V-

- ? A- J *

N —

>

\-

>

X, V-• ( V )

(22) -5x + y = 5

(24) 4x + 2y = 8

4 y - 8 3(^.Z

16

Review Questions:

State the slope of each line:


1 1 ' Q \\

1 1 i

V \

0 T b

\ C J ^ 1

\ 0

. c 1 a

K J

-4 \

J -4

e 0 c

1

— 1 i

- 1 0 - 9 - 8 - 1 2 3 4 5 6 7 8 9 10 *

(1) a t^o sU^ie

(3) c 3

(5) e ?:€rO

(7) g ^

(9) i ^

(2) b

(4) d

(6) f

(8) h

(10) j

- ]

3

Find the slope of the line that passes through the two given points:

(11) (2, 5) and (3, 6) (12) (4,1) and (-4,1) (13) (4,1) and (-6, -4)

m = -f.—-

(14) (-2,4) and (10, 0) (15) (3, 2) and (3,-2) (16) (2, 7) and (-2, -3)

3 - 5

r p ) - n o -siejae.

2^

17

the value of r so the line that passes through the two points has the given slope:

( 1 7 ) ( 6 , 3 ) , ( r , 2 ) , m = |

(^~r _L »

(18) (r, 3), (-4, 5), m = - |

2- < - J i - ^

(19) (5 ,r ) , (2 , -3 ) , m = ^

^ ' 3

r ^ )

(20) (-2, 7), (r, 3), m = 1 "3 ' - 2 L - r

3 - - a

(21) (4, -5), (3, r), m = 8

- / 3

(22) (6,2), (9, r), m = - 1

r ^ - 1

( 2 3 ) ( 4 , r ) , ( r , 2 ) , m = - |

3 - r-<4

r ^ 7

(24) (r, 5), (-2, r), m = - |

^ " . . .

7

18

Review Questions:

For each line graphed below, complete the given table:


s y

\ ' r \

A 0 4 6 Jr >

• N s

-6-

slope X- and y-intercepts

linear equation in slope-intercept form

(1) r y -

(2) s

(3) t - t Algebraically f\r\d the x- and y-intercepts for each linear equation:

(4) 4x - 3y = 12 (5) 2 x - 5 y = 20 (6) x + 5y = 8 (7) 3 x - y = -7

State the slope and y-intercept of each linear equation:

(8) 5x + 2y = 7 (9) -2x + 3 y = 8 (10) 8 x - y = 12 (11) 7 x - 2 y = 9

cj= I x A- 1

X

2.

19

Write the linear equation in slope-intercept form that passes through each of the two given points:

(12) (3, 4) and (-1,-4) (13) (2, 5) and (0, 3)

^ ' - ^ ' 3 = U . ) , L

(14) (-3, 1) and (-1,-3)

t

(15) (-5, -2) and (1,-6)

- - - f i t . - ^

(16) ( - 5 ® and (4,(5)

n o - 3 - 3 3^o(-^)4't > 3^oC<t3vb

0

(17) @ 4) and ^ 2 )

o

20

What Did the Policeman Tell The Burglar ih the Bathroom? Find the answer for each exercise in the adjacent answer columns. Write

l ## the letter of the exercise in the box containing the number of the answer. art 1. Write the equation of the line indicoted.

J7U Equation of AB

2- 0 Equation of CD

l \ Equation of E F

'-^ S Equation of GH

\ > 1̂ E

\ Si

F

>

\

Port 1 Answers

I II y = | x + l

2 •3

_ 3

Part 2. Write the slope of a line parallel to the given line.

5 T u = ^ x - 2 26 U y = 8 -3x

5 2 4 y = - f x - 2

O 2 y = - | x - 2

Part 2 Answers

6̂ 0 -5x + y = 12 /̂ A 4A: + 7y = 21 0 6 5 A 21 - | 0 2 6 - 3

Part 3. Write the slope of a line perpendicular to the given line. Part 3 Answers

- q E y = - | x + l i 3 H y = 6 x + l l J23 - 1 HI3 - i

i(a0 2x + 5y=40 Z 3 T 8 A : - 3 y = 1 5 0 16 1

i Part 4. Write an equation for the line that is parallel to the given line I j i ^ and that contains the given point. Part 4 Answers

J^Jt y = 3x - 4; (2. 7) C 1 y = - 4 x +1 W y = | x - 3

iCV y = - ^ x + 5 ; ( 4 , - 5 ) U>IO y = 3A: +1

1 C 4x + y = - 9 ; ( -2 ,9)

1 ^ R -5x + 3y = 6; ( -3 , - 8 ) y i S y = 4 x - 3 P27 y = - X - 4

P x + y = 7 ; ( - 4 , 0 )

Part 5. Write an equation for the line that is perpendicular to the given line and that contoins the given point.

7 U y = - | ^ + 4 ; (2 .5 )

2 T y = f x - 3 ; ( 2 , - 3 )

L o P y = f + 1 5 ; ( - 3 . 7 ) ,

3 M 3x + 2y = -10; (-9, - 2 )

-2 N 5A: - y =16; (O, O)

Part 5 Answers

P 20 y = -4:X - 5

\JlA^^;=Ne^o«e^ T I 2 y = - f x + 2

l R ^ i L ' ' ^ \ : 4 ^ ^ \ y 3 ' U 7 y = 3A: - 1

- - - - ^ s v ^ o | w e - -Ny22 y = 4 ^

I

2

o 3 4 6

O 7

U r to

u 3 i n 12

T IS 14

22

15

I

16

O 17

0 20

P

21

ft

22 23

r

2 4

5

2 5 2 6

U

2.

, ] - i T y +^ ' ' 2 •

. - ^ u ^ -x - t - 7

1^ j = ' i x + - ^ j a r ^ )

- 3 - ' € ( 0 ^ ^

- :^X f

-7 / i- •+ b ;

- 2 . - ^(o +fc

unit 1: linear equation s - wikispacesunit+1-+linear... · f x (6) x - 3y = 8, with a y ... write...

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