Algebra II Name:

Worksheets

Worksheet #1 (§3 – 2) Rewriting Linear Equations

Rewrite each linear equation in Slope-Intercept Form. (See Notes, p.3) 1.

€

2 x + 3y = 4

2.

€

3x − y = 2

3.

€

x + 5y = 10

4.

€

x − y = 3

5.

€

x + y = −2

6.

€

5x + 6y = 30

7.

€

3x + 2y = 6

8.

€

3x − 5y = 15

9.

€

x + 2y = 5

10.

€

3x − 4y = 2

Rewrite each linear equation in Standard (General) Form.

11.

€

y =1

2x − 3

12.

€

y = x − 4

13.

€

y = −x + 5

14.

€

y = 2 x − 7

15.

€

y =2

3x − 4

16.

€

y = −5

2x −

3

2

17.

€

y = −6x + 1

18.

€

y =3

5x − 1

19.

€

y = −3

4x +

1

2

20.

€

y = 3x −1

2

SLOPE-INTERCEPT FORM

€

y = mx + b

or

€

y = ___ x ± ___

the coefficient of y must be positive 1.

STANDARD (GENERAL) FORM

€

Ax + By = C

or

€

___ x ± ___ y = ____

A, B and C must be integers (not fractions).

A must be positive.

Answers: 1.#y = −

23x + 4

3##3.#y = −

15x + 2##5.#y = −x − 2##7.#y = −

32x + 3

9.#y = −12x + 5

2##11.#x − 2y = 6##13.#x + y = 5##15.#2x − 3y = 12

17.#6x + y = 1##19.#3x + 4y = 2

Algebra II Name:

Worksheets

Worksheet #1 (§3 – 2) Rewriting Linear Equations – Version 2

Rewrite each linear equation in Slope-Intercept Form. (See Notes, p.3) 1.

€

2 x − 3y = 8

2.

€

3x − y = 1

3.

€

x − 5y = 1

4.

€

x + y = 2

5.

€

x − 2y = −2

6.

€

6x − 5y = 30

7.

€

2 x − 3y = 6

8.

€

5x + 3y = −15

9.

€

x − 2y = −3

10.

€

4x − 3y = −9

Rewrite each linear equation in Standard (General) Form.

11.

€

y = −1

2x +

5

2

12.

€

y = x + 4

13.

€

y = −x +1

3

14.

€

y = 2 x +1

2

15.

€

y = −2

3x + 2

16.

€

y = 6x − 3

17.

€

y = −0.5x + 1

18.

€

y =3

5x −

1

2

19.

€

y =3

2x +

1

4 20.

€

y = 2 x −1

3

SLOPE-INTERCEPT FORM

€

y = mx + b

or

€

y = ___ x ± ___

the coefficient of y must be positive 1.

STANDARD (GENERAL) FORM

€

Ax + By = C

or

€

___ x ± ___ y = ____

A, B and C must be integers (not fractions).

A must be positive.

Algebra II Name:

Worksheets

Worksheet #2 (§3 – 3) Slope of a Line PART 1 Find the slope of the line through the given points. 1.

€

8 , 4( ) , 6 , 5( ) 2.

€

0 , 7( ) , 2 , 3( ) 3.

€

−2 , −3( ) , 0 , −1( ) 4.

€

−8 , −7( ) , −6 , −4( ) 5.

€

−4 , 2( ) , −6 , 5( ) 6.

€

−5 , 3( ) , 6 , 5( ) 7.

€

6 , 3( ) , 2 , 0( ) 8.

€

0 , −3( ) , 3 , −1( ) 9.

€

2 , 4( ) , −3 , 4( ) 10.

€

−6 , 3( ) , −4 , 5( ) 11.

€

−4 , 3( ) , 4 , 9( ) 12.

€

4 , 8( ) , 1 , 3( ) 13.

€

5 , −2( ) , 5 , 0( ) 14.

€

7 , −6( ) , −5 , 2( ) 15.

€

1 , 2( ) , −3 , −4( ) Find the slope of the line with the given equation. 16.

€

y = 2 x − 1 17.

€

3x + 2y = 6 18.

€

y = 3x − 2

19.

€

2 x + 5y = 10 20.

€

y = 3 21.

€

y + 4 = 0

22.

€

y = 8 − 2 x 23.

€

3x − 5y = 10 24.

€

x = 2

25.

€

y + 4x = 12 26.

€

y +1

5x = −2 27.

€

y + x = 0

28.

€

y − 3 = −2

3x 29.

€

x − 3y = 9 30.

€

3x − 5 = 0

31.

€

3x = 2y − 6 32.

€

y = −4x 33.

€

3x − y = 6

34.

€

2 x − y = −4 35.

€

y = 9 − 3x 36.

€

x = 8 − y

37.

€

3x + y = 8 38.

€

6x + 4y = 8 39.

€

x + 5y = 5

40.

€

4x − 3y = 9 41.

€

3y − 9 = −2 x 42.

€

3x − 5y = 5

43.

€

y =2

5x + 3 44.

€

y = −5x − 2 45.

€

y = x − 4

PART 2

For #16 – 45, find the coordinates for y-intercept of the line with the given equation. Answers:

1.#− 12##3.#1##5.#− 3

2##7. 3

4##9.#0##11.# 3

4#13.#undefined##15.## 3

2##17.#− 3

2#19.#− 2

5##21.#0##

23.# 35##25.#−4##27.#−1##29.# 1

3##31.# 3

2##33.#3##35.#−3##37.#−3##39.#− 1

5##41.#− 2

3##43.# 2

5##45.#1

Algebra II Name:

Worksheets

Worksheet #4 (§3 – 4) Equations of Lines Find an equation, in slope-intercept form, of the line having slope m and y-intercept b.

1.

€

m = 4 , b = 8 2.

€

m =4

3, b = 0 3.

€

m = −6 , b = 1

4.

€

m = −1

5, b = 3 5.

€

m = −8 , b = 11 6.

€

m = −11 , b = 13

Find an equation, in slope-intercept form, of the line having slope m and y-intercept b. Then rewrite each equation in standard form.

7.

€

m = −2 , b = −6 8.

€

m = −9

5, b = −7 9.

€

m =3

7, b = −1

10.

€

m = 9 , b = 4 11.

€

m =2

9, b = 0 12.

€

m = −7

2, b = −6

Write an equation in standard form of the line containing the given point and having slope m. (Hint: Use the point-slope formula first and then rewrite the equation in standard form.)

13.

€

−2 , 3( ) , m = −1 14.

€

4 , 7( ) , m =3

2 15.

€

−2 , 3( ) , m = 4

16.

€

0 , −7( ) , m = −4 17.

€

7 , 5( ) , m = 0 18.

€

−6 , 7( ) , m = −1

2

19.

€

1 , 2( ) , m undefined 20.

€

6 , 2( ) , m =3

4 21.

€

5 , −3( ) , m = −2

Answers: 1.#y = 4x + 8##3.#y = −6x + 1##5.#y = −8x + 11##7.#2x + y = −6##9.#3x − 7y = 711.#2x − 9y = 0##13.#x + y = 1##15.#4x − y = −11##17.#y = 5##19.#x = 1##21.#2x + y = 7

Algebra II Name:

Worksheets

Write an equation in standard form of the line containing the given points. (Hint: Use

€

m =y 2 − y 1

x 2 − x 1

to calculate slope. Then use the point-slope formula first and

then rewrite the equation in standard form.)

22.

€

5 , 7( ) , 6 , 8( ) 23.

€

4 , 2( ) , −4 , −2( ) 24.

€

8 , −2( ) , 14 , 1( ) 25.

€

−3 , 6( ) , 3 , −6( ) 26.

€

1 , 2( ) , 3 , 8( ) 27.

€

0 , 5( ) , −3 , 2( ) 28.

€

−3 , 4( ) , 1 , 6( ) 29.

€

11 , 7( ) , 9 , 3( ) 30.

€

21 , −2( ) , 27 , 2( ) 31.

€

2 , −5( ) , 0 , −7( ) 32.

€

−3 , 4( ) , 3 , 8( ) 33.

€

−2 , −6( ) , 8 , 4( ) Answers: 23.$x − 2y = 0$$25.$2x + y = 0$$27.$x − y = −5$$29.$2x − y = 15$$31.$x − y = 7$$33.$x − y = 4

Algebra II Name:

Worksheets

Worksheet #5 (§3 – 4) Parallel and Perpendicular Lines For each equation, determine the following:

(a) The slope of a line that is PARALLEL to this line, and (b) The slope of a line that is PERPENDICULAR to this line.

1.

€

y =3

2x + 7 2.

€

y =4

5x − 2 3.

€

y = −3

8x + 5

4.

€

2 x + y = 3 5.

€

3x − 5y = 110 6.

€

y = −x

7.

€

y = 1 8.

€

x = 3 9.

€

x − 3y = 8

10.

€

y = 8 − 2 x 11.

€

3x − y = 6 12.

€

x + 5y = 5

13.

€

2 x − y = −4 14.

€

y =3

4x + 2 15.

€

3x = 5 − y

Answers: 1.# a( ) 32 # b( ) − 2

3##3.# a( ) − 3

8b( ) 83 ##5.# a( ) 35 b( ) − 5

3##7.# a( )0 b( )undefined##9.# a( ) 13 b( ) − 3

11.# a( )3 b( ) − 13##13.# a( )2 b( ) − 1

2##15.# a( ) − 3 b( ) 13

Hint: First, find the slope of the given line. Then remember…

• Parallel lines have equal slopes

• Perpendicular lines have slopes that are opposite reciprocals.

Algebra II Name:

Worksheets

Worksheet #7 (§9 – 1) Distance and Midpoint Formulas

Use the distance formula: d = x 2 − x1( )2+ y 2 − y1( )

2 to find the distance

between the given points to the nearest hundredth. 1.

€

4 , 7( ) , 1 , 3( ) 2.

€

4 , 2( ) , −4 , −2( ) 3.

€

8 , −2( ) , 14 , 1( ) 4.

€

−3 , −8( ) , −7 , 2( ) 5.

€

0 , −4( ) , 3 , 2( ) 6.

€

0 , 9( ) , −7 , −2( ) 7.

€

−13 , −9( ) , −1 , −5( ) 8.

€

4 , −6( ) , 3 , −9( ) 9.

€

−2 , 5( ) , 7 , 14( ) Use the midpoint formula:

€

x 1 + x 2

2,

y 1 + y 2

2

"

# $ $

%

& ' ' to find the coordinates of the

midpoint of a line segment with the given endpoints. 10.

€

2 , 4( ) , 6 , 8( ) 11.

€

−2 , 6( ) , 8 , 6( ) 12.

€

−4 , −7( ) , 2 , 1( ) 13.

€

8 , −3( ) , 5 , 4( ) 14.

€

−1 , 4( ) , 5 , −4( ) 15.

€

12 , 3( ) , −3 , 1( ) 16.

€

0 , 9( ) , −7 , −2( ) 17.

€

−13 , −9( ) , −1 , −5( ) 18.

€

20 , 4( ) , −6 , −16( ) Answers: 1.#5##3.#6.71##5.#6.71##7.#12.65##9.#12.73##11.# 3,6( )13. 6.5, 0.5( )#15.# 4.5,2( )##17.# −7,−7( )