Linear Equations Reteach

Linear Equations Reteach

Name ________________________ Date _____________ Period ______

0. The following equation y = mx + b is called what? (write a sentence, do not use pronouns)

1. What does the “m” represent? (write a sentence, do not use pronouns)

2. What does the “b” represent? (write a sentence, do not use pronouns)

3. What are all of the other words that also refer to slope that were mentioned in the Slope Intercept Reteach Video? (write a sentence, do not use pronouns)

4. Please list all of the ways to find slope that the Slope Intercept Reteach Video mentioned? (write a sentence, do not use pronouns)

5. The x-value of the y-intercept is always equal to what number? (write a sentence, do not use pronouns)

Determine the y-intercept, and slope of the following equations, then accurately graph the equations: 6.

2

y = x − 6

7.

3

y = −2 x − 3

8.

y = 6 x − 5

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________

Is the slope increasing or decreasing?



�

�

9

�

�

7

y = - x + 2

10.

4

�

�

y = -2 x + 3

11.

1

y = x + 7 3

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________




�

�

�

�

�

�

12.

y = 2 x − 1

13.

y = -6 x + 3

14.

y = 3 x − 2

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________




�

�

�

15.

3

y = x − 6

�

16.

2

�

y = 1 − 4 x

�

17.

y = 5 − 6 x

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________




�

�

�

�

�

�

18

3

y = - x

19.

4

y = -4

20.

1

y = x 4

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________




�

�

�

21.

y = 3

�

�

22.

y

=

�

23.

6 - 5x

2

y = 3 + x 5

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________




�

�

�

�

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Directions: Direction s: Given the graph, determine the slope (m), and y-intercept (b), then write the equation of the line in slope intercept format. �

24.

slope =____________

Is the slope positive or negative?

y-intercept =________ =________

What is the rise? �

y =

What is the run?

�

25.

slope =____________


y-intercept =________ =________


y =

What is the run?

�

26.

slope =____________


y-intercept =________ =________


y =

What is the run?

�

27.

slope =____________


y-intercept =________ =________


y =

What is the run?

�

28.

slope =____________


y-intercept =________ =________


y =

What is the run?

�

29.

slope =____________


y-intercept =________ =________


y =

What is the run?

30. The following function, Ax+By=C , is known as what? (write a sentence, do not use pronouns) pronouns)

31. If a linear equation is in the following format Ax+By=C a) What is the formula formula for determining determining the x-intercept? x-intercept?

b) What is the formula for determining the y-intercept?

c) What is the formula formula for determining determining the slope?

Determine the x-intercept, y-intercept, and the slope of the following equations. Reduce all fractions. 32.

4x +10 +10y =80

33.

8x+5y=120

34.

3x+y=21

X-int:_________

X-int:_________

X-int:_________

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________

35.

6x-y=18

36.

5x -2y -2y = -30

37.

2x-7y=28

X-int:_________

X-int:_________

X-int:_________

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________

38.

-3x + 4y =24

39.

-20x+ -20x+ 15y 15y = -60

40.

-2x +7y =28

X-int:_________

X-int:_________

X-int:_________

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________

41.

-x-6y=42

42.

-5x-2y = -40

43.

-9x -6y = 72

X-int:_________

X-int:_________

X-int:_________

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________

44.

3x-12y 3x-12y =18

45.

10x -8y = -4

46.

-2x+7y=31

X-int:_________

X-int:_________

X-int:_________

Y-int:_________

Y-int:_________

Y-int:_________

Slope:_________

Slope:_________

Slope:_________

Solving for Y Step 1: Get rid of parenthesis 1.

3( x + 2 y ) = 7 x + 2 y

4.

−

7.

3(5 x +

3(2 x + y ) = 7 x + 2 y

2 3

y) = 7 x + 2 y

2. 4( 2 x −

5. 5 x

8. 4(

3. 2( x +

y ) = 8x

6.

4 (3 x − 2 y )

= −

1 4

x + 10 −

3 4

y ) = 3( 3(10 x + 20 y )

2( − x + y ) = −(11x + 3 y )

−

9.

y ) = 8x

−

1 2( x − 4 y ) = 7(11x + 3 y ) 2

Step 2: Get rid of fractions 1.

1

x + 2 y

3

5.

2 x +

7 10

=

y

10 + y

=

5+ y

2. 3 x −

5 2

y

6. 2 x − 8 y

=

=

3.

7 + 4x

−

4 + 9 x

7.

2

x − 5 y

5 4

=

y − x

3 + 8 x

=

4. 10 x +

4

9 + 4x

8.

1 5

x − 7 y

y

=

=

2

5

−

2

−

3x

Step 3: Combine Like terms 1.

3 x + 5 x + 7 = 5 y + 9 − 5 y

4.

−

7.

3 + 5 x + 7 y

3 x + 5 y + 4 x

=

=

5y + 9

5x − 9 x

2. 10 x + 9 y − 8 x

5. 2 x + 5 y

8. 13 + 8 y

−

−

8y

7

=

=

=

5 + 4x − 8

5 + 4x − 2

6x − 5 − 6x

3. 10 y + 2 x + 3 + 2 y

6.

y + 2 y + 3x + 2 y

9. 10 y − 2 x + 3 + 2 x

=

=

9 + x − 5x

9 + 2x

=

9y

+

−

7

8 − 5x

−

x

Solving for Y Step 4: Move smaller Y to the other side. 1.

5 y + 3 x

5.

−

2 y − 7 x +1

=

5 y + 3x

2 y − 7 x +1

= −

2. 7 y + 3 x

6.

=

7 y + 3 x

−

10 y + 8

10 y + 8

= −

3. 5 y + 3 =

4.

9y + x

−

7. 5 y + 3 = 9 y

+

−

3 y + 5 x

8. 3 y + 5x

x

4y + 7

= −

=

4y + 7

Step 5a: Move the other variable (x) to get the y alone. 1.

6 x + 5 y

=

10 x + 9

2.

5.

5 y + 7 x

=

9

6.

3 x − 2 y

=

50

9.

5 y + 4 x

=

9 + 4x

10. 10 x + 2

=

8x + 7 y

−

10 x

=

−

3 x + 2 = 5 x − 27 y

−

3.

7.

17 y + x

9x + 2

4.

8 x + 2 = y − 5 x

2

8.

82 = − y − 5 x

= −

17 y + 8x

= −

11. 17 y − x

9x + 2

= −

12.

y + 7x

Step 5b: Move the constant to get the y alone. 13.

y − 3 = 5 x + 10

14.

y + 8 = 5x + 20

7−y

18.

−

y + 11 = x − 10

22.

x + 2 = 10 y − 3

17. 8 x

21.

=

3 + y

=

5 x + 10

15.

5 x − 7 = 2 y + 3

−

19. 2 y + 3 =

23.

5x + 3

−

y + 13 = x + 7

16. 4 y + 15

20. 7 x + 2

=

=

5 x + 12

4y + 5

24. 4 y + 1 = 5 x

−

99

Solving for Y Step 6: Get rid of the y’s coefficient by division. 1.

2 y

=

8 x − 10

2.

5.

5 y

=

8 x − 20

6. 9 y

=

10.

12 y

9. 10 y

=

25 x + 70

3 y

−

−

9 x − 12

3.

−

72 x − 18

7.

−

=

42 x + 36

= −

4 y

4.

18 x − 16

=

y = −7 x + 6

11.

14 y

−

=

18 x − 28

9 x + 13

y

= −

8. 6 y

= −

−

12.

9 x + 30

y = − x + 5

−

Step 7: Reduce 1.

y

=

8 x 12

−

5.

9.

y

y

=

=

8 x 5

−

25 x 10

48

−

2.

12

y =

18 x − 16

−

20

6.

5

+

70 10

−

y

=

4

10.

y

=

y

=

7 x

−

3

+

−

72 x − 18 −

3.

7.

9

y

=

7 x

−

−

42 x + 36

−

12

−

11.

y =

1

+

18 x −

14

12

4.

3

6

8.

1

y

=

y

=

11 x + 20 5

9 x + 30

−

6

−

−

28 14

−

12.

y

=

x + 5

−

1

−

Solve for Y and Graphing Reteach WS Guided EXAMPLES

Name Date

Period

Please watch the videos on the student connections S: Files Directions: Direction s: Solve for y. Show the work, each step, that is needed to arrive at the solution. Determine the slope (m), and y-intercept (b), then graph the equation. � Your work is your answer! Example 1.

3 x − 2 y

−

10

= −

�

slope =____________ y-intercept =________ =________

�

Example 2.

2( 4 − 5 x ) + 3 y + 7

8x + 3

= −

�


Solve for Y and Graphing Reteach WS

Name Date

Period

Directions: Direction s: Solve for y. Show the work, each step, that is needed to arrive at the solution. Determine the slope (m), and y-intercept (b), then graph the equation. � Your work is your answer! 1. 2 x + y = 7

�


�

2. 4 x − y = −6

�


�

3. 4 x + 2 y = 8

�

slope =____________ y-intercept =________ =________ �

4. 6 x − 4 y = −24

�


�

5. 3 x − 4 y = 8 − 5 y

�


�

6. −2 x − y

=

8 + 3y

�

slope =____________ y-intercept =________ =________ �

7. x − y = 6 − 4 x

�


�

8. −2 x − 6 y = 36 + 4 x

�


9. 3( x − 2 y ) = 12 − 5 x �

�


10.

−

8 3

x + 3 y

2x − 4

= −

�

�


Linear Equations Reteach

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