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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( )