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Unit 3 Vocabulary
• Parallel Lines
• Perpendicular Lines
• Solution of a System of Linear Equations
• Slope
• Standard Form
• Slope Intercept Form
• System of Equations
• System of Inequalities
1
Writing Linear Equations
Point-slope formula:
y – y1 = m (x – x1)
a) Label your point (x1, y1)
b) Plug the point into the point slope equation
c) Distribute and simplify
Write an equation in slope intercept form using the given information.
Examples:
1) (4,-3) m = 5
2) (6, 2) m = 2/3
3) (-3, 4) (0, 0)
4) ( 2,-7) (0, -5)
Practice
3
10
1) (-2, 3) m = -4
2) (8, 6) m = ¼
3) (5, -6) m =
4) (3,3) (0,2)
5) (-1, 0) (0,4)
6) (4, 2) (0,3)
2
Practice
1)
(1, 2), slope = 7
2)
( 3, −1), slope = −1
3) (1,1) and (-4,16)
4) (−2, 5), slope = −4
5) (3, 5), slope =5/3
6) (8,9) and (-6, 2)
7) (4, 1), slope =1/2
8) (2, 5), slope = 0
9) (2, 8) and (3, 6)
10) (7, -3) m = 2/7
11) (−8, 2), slope = ¼
12) (6, -2) and (9, -3)
13) (-1, 3) and (3, -9)
14) m = 2/3;
15) (8,4) and (5, 10)
(6,5)
3
Standard Form verses Slope Intercept Form
•
•
Standard Form: The standard form of a linear equation is Ax + By = C; where A,B and C are real
numbers and A and B are not both zeros.
Slope Intercept Form: A linear equation of the form y=mx + b is written in slope-intercept form where
m is the slope and b is the y-intercept of the equation’s graph
Write the standard form of the equation.
1) 2y = -7x + 5
2) -6x = 7y – 2
3)5 – 6x = 2y
4) -6 – 10x = 4y
5) 2y = 4x – 2
6) 12 – 3x = 5y
Write the slope intercept form of the equation.
1) 2y + x = 4
2) 3x – 2y = 5
3) -3x – 4y = 12
4) y + x = 2
5) y – 2x = 0
6) 2y = 4x - 6
4
Practice
Write the equation in the indicated form.
1) 3x – 2y = -16; Slope Intercept
2) 12 – 4x = 5y; Standard Form
3) 9x – 7y = -7; slope intercept
4) -7x – 14 = 21y; Standard Form
5) x – 3y = 6; Slope Intercept
6) 4x – y = 1; Slope Intercept
7) 4y -6x = 8; Slope Intercept
8) y = -2x + 5; Standard Form
9) 10 – 12y = 14x; Standard
10) 24 – 10x = 12y; Standard
11) 6x – 3y = 12; Slope Intercept
12) 30 – 10y = 5x; Slope Intercept
5
Parallel and Perpendicular Lines
Use the information to write an equation of a line that is parallel to the line that is given.
1)
(-3, -5) y = 3x – 5
2) (-2, 11) y = -x + 5
3) (-1,3); 2y - 2x = 2
Use the information to write an equation of a line that is perpendicular to the line that is given.
1) (4, -5); y = 2x + 3
2) (4, 3); 2y = 4x – 8
3) (-1, -3); 3y - x =6
Practice
Use the information to write an equation of a line that is either parallel or perpendicular to the line that is given.
1) (-1, 3) Parallel to
2) (6, 8) Perpendicular to
3)
(3, -3) Perpendicular to
ହ
y = 2x + 2
y= x + 5
y=- + 10
ଶ
4)
(5, -1) Parallel to
y = -3/5x -3
5)
(-9, 2) Perpendicular to
y = 3x – 12
6)
(-1, 2) Parallel to
y = 2x + 2
6
7)
8) (5, 1) Perpendicular to
2y = 4x - 6
(1,7) Parallel to
y = 6x – 1
9) (3, 3) Perpendicular to
2y = 3x - 6
11) (-2, 5) Parallel to
y=½x–3
13) (9, 4) Parallel to y –x = 3
14) (8, -1) Perpendicular to
4y + 2x =12
9)
(-2, 2) Parallel to
2 y = -2x - 4
12) (-5, 2) Perpendicular to
y + 3 = 2x
15) (-10, 0) Parallel to
–y + 3x = 16
Writing Linear Equations in Slope Intercept and Standard Form
Use the given information to write an equation in slope intercept form and standard form.
1) M = -3; (2,-2)
2) m = 1 (-3, 2)
3) (-8, 4) (4, -4)
4) (-5, 2) (-4, 3)
7
Practice
Use the given information to write an equation in slope intercept form and standard form.
1) m = -2; (0, 5)
2) m = 3; (4, -1)
3) (-6, -2) (-1, -2)
4) (10, 6) (-12, -5)
5) M= -4; (-8, 0)
6) (3, 9) (1,1)
7) M = -3/2 (-4, -4)
8) M = 1/6 (-6, -10)
9) (0,2) (, 5)
10) M = 3; (2, 5)
11) M = -2; (-1, 4)
12) M = -5; (0, -7)
8
Systems of Equations
A system of linear equations consists of two or more linear equations in the same variables. A solution of a
system of linear equations in two variables is an ordered pair that satisfies each equation in the system.
Solving Linear Systems by Graphing
Solve the Linear System by Graphing; be sure to check your answers and state the number of solutions.
1) Y = 5x
2) y = x + 7
3) y= x + 5
Y = -5x + 10
y = -1/4x – 2
y= -2x + 8
y
y
y
x
4) x – y = 4
4x + y = 1
5) 2y = 4x -4
y = 2x – 2
y
6)
y = -2x -5
2y = 4x - 16
y
y
x
x
x
x
x
9
Practice
Solve linear systems by graphing, be sure to check your answer and state the number of solutions
1) Y= -5/3x + 3
2) Y = 4x + 3
3) Y = -1/2x – 1
Y = 1/3x – 3
Y = -x - 2
Y= 1/4x - 4
y
y
y
x
x
4) Y = -1
Y = -5/2x + 4
5) Y = 3x – 4
Y = -1/2x + 3
x
6) Y = -2x + 2
Y = -2x - 2
y
y
y
x
x
7) Y = -1/2x – 2
Y = -3/2x + 2
8) Y = 1/3x – 3
Y = -x + 1
y
9)
y
x
x
y = -3x – 9
3y = -6x – 3
y
x
x
10
11) Y = x + 2
X = -3
10) Y= -3x + 4
Y = 3X – 2
12) X – y = 3
7x – y = -3
y
y
y
x
x
13) 4x + y = 2
X–y=3
14) Y= -x + 1
Y = 2x - 5
x
15) -x + y = 5
2x + y = 8
y
y
y
x
x
16) -6y = 3x – 12
Y = -1/2x +2
x
17) X – y = 3
X + 2y = -6
y
18) X + y = -2
-x + y = 6
y
y
x
x
x
11
Solving Systems of Equations by Elimination
Solve the following systems of equations using the elimination method; be sure to check your
answers.
1) X + 3y = 8
4x – 3y = 2
4) 4x + 2y = 10
X – y = 13
7) 5x + 2y = 16
3x – 4y = 20
8)
2) 2x + y = 5
-2x + 3y = 8
5) 5x -2y = -2
-x – 2y = _14
3) X + 7y = 0
2x – 8y = 22
6) 8x – 6y = -20
-16x + 7y =30
6x + 5y = 19
2x + 3y = 5
9) 4x + 5y = 35
2y – 3x = -9
12
Practice
Solve the following systems of equations using the elimination method; be sure to check your
answers.
1) X + 2y = 3
-x + 3y = 2
4) 2x – 9y = 1
7x – 12y = 23
7) 4x + 3y = 8
X – 2y = 13
2) 2x + 3y = 11
-2x + 5y = 13
5) x + y = 2
2x + 7y = 9
8) 6x + y = -10
5x + y = -10
3) 4x + 3y = 2
5x + 3y = -2
6) 3x – 2y = 3
-x + y = 1
9) 10x – 9y = 46
-2x + 3y = 10
2
10) -3x – 5y = -7
-4x + 5y = 14
11) 8x – 5y = 11
4x – 3y = 5
12) 9x + 2y = 38
3x – 5y = 7
13) x + y = 4
-3x + y = -8
14) x + 3y = 10
3x – y = 13
15) 4x – 9y = -21
4x + 3y = -9
16) x – y = -4
x + 3y = 4
17) -9x + 4y = -17
9x – 6y = 3
18) 2x – 3y = -5
5x + 2y = 16
3
Writing Equations Practice Test
I.
Name: _______________________
Date: _________ Period: ________
Use the point-slope equation to write an equation of the line in slope-intercept form.
1) m = 2/5;
(-10, 3)
4) (-2, 12) (6, 28)
II.
2) m = -4;
(8,-3)
3) (8, 4) (5, 10)
5) (8, 4) (10, 12)
6) (-1, 3) (3, -9)
Use the given information to write an equation in slope intercept form and standard form.
7) m = -2; (-2, -4)
8) m = ½ ; (-4, 6)
9) m = undefined (-2, 4)
10) (7, 10) (2, 30)
11) (-3, 16) (-5, 20)
12) (-2, 5) (1, 5)
III.
13)
Write the standard form of the equation.
Y = 2x – 6
14)
6y – 10 = 5x
15) -8 + 29x = 12y
16) 12y – 4= 10x
IV.
Use the information to write an equation of a line that is either parallel or perpendicular to the
line that is given.
19) (3, -3); y = x + 5; parallel 20) (5,1); y = 5x – 2; Perpendicular
21) (-2,5); y = 2x – 3; Parallel
22) (9, 4); y =x + 3; Parallel
ସ
23)(-4, -1); y= ଷ ‫ݔ‬+ 6; Perpendicular 24) (-9, 2); y = 3x – 12; perpendicular
4
V.
25)
Solve the Linear System by Graphing; be sure to check your answers and state the number of
solutions.
-x + y = 9
26)
-x + y = 9
27) y = -5x - 2
X+y=1
x–y=9
2y = -10x -4
y
y
y
x
x
x
28) y = -3x + 1
Y=x-7
29) -2x + y = 1
2x + y = 5
30) y = 3x + 4
y = -2x – 1
y
y
y
x
x
x
VI.
Solve the following systems of equations using the elimination method; be sure to check your
answers
31) 4x-3y = 5
32)
7x – 2y = 5
33) x + y = 1
-2x + 3y = -7
7x – 3y = 4
-2x + y = 4
34) 3x + y = 21
X+y=1
35) x + 3y = 1
5x + 6y = 14
36) 2x – 3y = -5
5x + 2y = 16
5