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MPM1D

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3.5 Graphing y=mx+b

Sketch the graph of each line.

1)

y

=

x

+ 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

2)

y

=

−5

3

x

+ 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

3)

y

=

−

x

− 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

4)

y

=

−4

x

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

5)

y

=

−4

5

x

+ 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

6)

y

=

1

2

x

− 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-1-

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7)

y

=

−

x

− 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

8)

y

=

x

+ 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

9)

y

=

−1

5

x

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

10)

y

=

−1

2

x

+ 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

11)

y

=

−2

x

− 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

12)

y

=

7

x

− 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-2-

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13)

y

=

−1

2

x

+ 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

14)

y

=

2

x

+ 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

15)

y

=

−3

x

+ 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

16)

y

=

8

5

x

− 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

17)

y

=

−5

4

x

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

18)

y

=

−2

x

− 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-3-

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19)

y

=

1

5

x

− 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

20)

y

=

−

x

− 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

21)

y

= 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

22)

y

=

3

2

x

+ 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

23)

x

= 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

24)

y

= 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-4-

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25)

x

= 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

26)

y

= −1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

27)

y

=

−

x

+ 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

28)

y

=

−

x

+ 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

29)

y

=

1

2

x

+ 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

30)

y

=

−5

2

x

− 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-5-

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MPM1D

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3.5 Graphing y=mx+b

Sketch the graph of each line.

1)

y

=

x

+ 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

2)

y

=

−5

3

x

+ 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

3)

y

=

−

x

− 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

4)

y

=

−4

x

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

5)

y

=

−4

5

x

+ 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

6)

y

=

1

2

x

− 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-1-

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7)

y

=

−

x

− 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

8)

y

=

x

+ 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

9)

y

=

−1

5

x

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

10)

y

=

−1

2

x

+ 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

11)

y

=

−2

x

− 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

12)

y

=

7

x

− 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-2-

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13)

y

=

−1

2

x

+ 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

14)

y

=

2

x

+ 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

15)

y

=

−3

x

+ 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

16)

y

=

8

5

x

− 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

17)

y

=

−5

4

x

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

18)

y

=

−2

x

− 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-3-

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19)

y

=

1

5

x

− 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

20)

y

=

−

x

− 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

21)

y

= 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

22)

y

=

3

2

x

+ 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

23)

x

= 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

24)

y

= 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-4-

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25)

x

= 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

26)

y

= −1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

27)

y

=

−

x

+ 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

28)

y

=

−

x

+ 4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

29)

y

=

1

2

x

+ 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

30)

y

=

−5

2

x

− 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

-5-

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MPM1D

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3.6 Graphing - given intercepts

Sketch the graph of each line.

1) x-intercept = 1, y-intercept = −4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

2) x-intercept = −3, y-intercept = 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

3) x-intercept = 1, y-intercept = 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

4) x-intercept = 3, y-intercept = 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

5) x-intercept = 4, y-intercept = −2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

6) x-intercept = −5, y-intercept = 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

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MPM1D

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3.6 Graphing - given intercepts

Sketch the graph of each line.

1) x-intercept = 1, y-intercept = −4

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

2) x-intercept = −3, y-intercept = 1

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

3) x-intercept = 1, y-intercept = 2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

4) x-intercept = 3, y-intercept = 3

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

5) x-intercept = 4, y-intercept = −2

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

6) x-intercept = −5, y-intercept = 5

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

−6

−5

−4

−3

−2

1

2

3

4

5

6

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MPM1D

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3.7 Writing Equations

Write the slope-intercept form of the equation of each line given the slope and y-intercept.

1) Slope = −4, y-intercept = −4 2) Slope = 6, y-intercept = 1

3) Slope = −2, y-intercept = −14) Slope =

−8

5, y-intercept = −3

Write the slope-intercept form of the equation of each line.

5)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

6)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

7)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

8)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

9)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

10)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

-1-

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11)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

12)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

13)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

14)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

15)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

16)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

17)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

18)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

-2-

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Answers to 3.7 Writing Equations

1)

y

=

−4

x

− 4 2)

y

=

6

x

+ 1 3)

y

=

−2

x

− 14)

y

=

−8

5

x

− 3

5)

y

=

−9

x

+ 56)

y

=

−3

2

x

− 5 7)

y

=

1

2

x

− 1 8)

y

=

1

3

x

9)

y

= 2 10)

y

= 5 11)

y

= 4 12)

y

=

−5

x

− 2

13)

y

=

−

x

14)

y

=

7

3

x

− 415)

y

=

−

x

+ 316)

y

=

2

5

x

− 4

17)

y

=

2

x

+ 518)

y

=

6

5

x

+ 2

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MFM1D

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3.7 Writing Equation of the Line (2)

Write the slope-intercept form of the equation of each line.

1)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

2)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

3)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

4)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

5)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

6)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

7)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

8)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

-1-

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9)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

10)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

11)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

12)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

13)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

14)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

15)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

16)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

17)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

18)

−5 −4 −3 −2 −1 0 1 2 3 4 5

−4

−2

2

4

-2-

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Answers to 3.7 Writing Equation of the Line (2)

1)

y

=

−4

x

2)

y

=

5

4

x

+ 13)

y

=

−

x

+ 5 4)

y

=

−

x

− 5

5)

y

=

−7

3

x

+ 46)

y

=

−

x

− 1 7)

y

= 1 8)

y

= 3

9)

y

= 5 10)

y

=

7

x

− 311)

y

=

8

5

x

− 5 12)

y

=

1

2

x

− 2

13)

y

=

−3

5

x

− 2 14)

y

=

−5

3

x

− 1 15)

y

=

5

4

x

16)

y

=

x

+ 3

17)

y

=

−3

x

+ 518)

y

=

−3

2

x

− 2

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3.8 Writing Equations (m & point)

Write the slope-intercept form of the equation of the line through the given point with the given slope.

1) through: (−2, −3), slope = 4 2) through: (−3, 3), slope = −2

3) through: (−4, 3), slope =

−7

4

4) through: (2, −4), slope = −1

5) through: (4, −2), slope = −16) through: (3, 1), slope =

5

3

7) through: (−4, 4), slope =

−9

4

8) through: (3, 0), slope = −1

9) through: (3, −2), slope =

−2

310) through: (5, 0), slope =

2

5

-1-

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11) through: (3, 2), slope = −112) through: (3, 3), slope =

1

4

13) through: (3, −4), slope = 914) through: (3, −1), slope =

−5

7

15) through: (3, 5), slope =

−3

216) through: (4, −4), slope =

−2

3

-2-

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Answers to 3.8 Writing Equations (m & point)

1)

y

=

4

x

+ 5 2)

y

=

−2

x

− 33)

y

=

−7

4

x

− 44)

y

=

−

x

− 2

5)

y

=

−

x

+ 26)

y

=

5

3

x

− 4 7)

y

=

−9

4

x

− 58)

y

=

−

x

+ 3

9)

y

=

−2

3

x

10)

y

=

2

5

x

− 211)

y

=

−

x

+ 512)

y

=

1

4

x

+

9

4

13)

y

=

9

x

− 3114)

y

=

−5

7

x

+

8

715)

y

=

−3

2

x

+

19

216)

y

=

−2

3

x

−

4

3

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MPM1D

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3.9 Writing Equations (2 points)

Write the slope-intercept form of the equation of the line through the given points.

1) through: (1, −4) and (0, −5) 2) through: (0, −2) and (3, −5)

3) through: (−1, −2) and (0, −2) 4) through: (0, −3) and (5, −1)

5) through: (0, −5) and (3, 0) 6) through: (−2, 3) and (0, −4)

7) through: (1, 1) and (0, 0) 8) through: (0, −1) and (−4, −2)

-1-

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9) through: (1, 1) and (1, 5) 10) through: (−1, 3) and (0, 3)

11) through: (4, 5) and (0, −1) 12) through: (3, 0) and (0, 3)

13) through: (0, 1) and (−2, −2) 14) through: (0, −4) and (3, 4)

-2-

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Answers to 3.9 Writing Equations (2 points)

1)

y

=

x

− 5 2)

y

=

−

x

− 2 3)

y

= −24)

y

=

2

5

x

− 3

5)

y

=

5

3

x

− 5 6)

y

=

−7

2

x

− 47)

y

=

x

8)

y

=

1

4

x

− 1

9)

x

= 1 10)

y

= 311)

y

=

3

2

x

− 112)

y

=

−

x

+ 3

13)

y

=

3

2

x

+ 1 14)

y

=

8

3

x

− 4

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3.10 Writing Equations (Parallel and Perpendicular)

Write the slope-intercept form of the equation of the line described.

1) through: (−1, 2), parallel to

y

=

−5

x

− 12) through: (−4, −1), parallel to

y

=

−1

4

x

+ 2

3) through: (5, 5), parallel to

y

=

6

5

x

− 14) through: (−1, −2), parallel to

y

=

−

x

− 5

5) through: (−1, −5), parallel to

y

=

x

+ 5 6) through: (−1, 3), parallel to

y

=

−2

x

+ 4

-1-

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7) through: (−2, −1), parallel to

y

=

−2

x

+ 58) through: (−1, 1), parallel to

y

=

−1

2

x

− 5

9) through: (3, −5), parallel to

y

=

−1

3

x

10) through: (−2, −3), parallel to

y

=

6

5

x

+ 4

11) through: (−2, 1), perp. to

y

=

x

+ 3 12) through: (−2, 5), perp. to

y

=

x

+ 4

-2-

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13) through: (3, 5), perp. to

y

=

−1

3

x

− 214) through: (1, −2), perp. to

y

=

−

x

− 5

15) through: (−2, −1), perp. to

y

=

−2

3

x

+ 316) through: (2, 0), perp. to

y

=

−

x

− 3

17) through: (−5, −1), perp. to

y

=

−5

6

x

− 218) through: (−1, −1), perp. to

x

= 0

19) through: (−3, −2), perp. to

y

=

3

x

− 320) through: (5, 5), perp. to

y

=

−5

7

x

− 3

-3-

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Answers to 3.10 Writing Equations (Parallel and Perpendicular)

1)

y

=

−5

x

− 32)

y

=

−1

4

x

− 2 3)

y

=

6

5

x

− 14)

y

=

−

x

− 3

5)

y

=

x

− 4 6)

y

=

−2

x

+ 1 7)

y

=

−2

x

− 58)

y

=

−1

2

x

+

1

2

9)

y

=

−1

3

x

− 4 10)

y

=

6

5

x

−

3

5

11)

y

=

−

x

− 1 12)

y

=

−

x

+ 3

13)

y

=

3

x

− 4 14)

y

=

x

− 315)

y

=

3

2

x

+ 216)

y

=

x

− 2

17)

y

=

6

5

x

+ 518)

y

= −119)

y

=

−1

3

x

− 3 20)

y

=

7

5

x

− 2

Unit 3 – Lesson 12 Worksheet

1. Gerry has a table of values representing a linear relation. Two of the numbers are hidden behind a ketchup spill. Determine the values that are hidden.

2. A boat is travelling from Point C toward Point D, which is on the shoreline. The shoreline is represented by the line through points A and B. Determine whether the path from C to D is perpendicular to the shore line. Justify your answer.

3. Write an equation of a line that has the same y-intercept as 2x + 3y – 6 = 0

4. The following table shows values for a linear relation. Write the equation for this line.

5. The table below represents a linear relation. Write the equation for this line.

6. Consider the equation y = mx + 5. If (7, 3) is a point on the line represented by this equation, find the value of m.

7. Determine the slope of the line representing each relation. Show your work.

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3.12 Systems

Solve each system by graphing.

1)

y

=

x

− 1

y

=

x

+ 2

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

2)

y

=

5

4

x

+ 4

y

=

5

4

x

+ 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

3)

y

=

−1

3

x

− 4

y

=

−1

3

x

− 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

4)

y

=

−1

2

x

− 3

y

=

1

2

x

+ 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

-1-

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5)

y

=

x

+ 2

y

=

−1

2

x

− 4

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

6)

y

=

2

x

+ 3

y

=

−3

x

− 2

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

7)

y

= 4

y

=

3

2

x

+ 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

8)

y

=

−1

3

x

+ 4

y

=

5

3

x

− 2

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

9)

−8

y

− 32 = 6

x

4

y

− 5

x

= 16

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

10)

4

5

y

=

−2

x

−

12

5

−4 −

x

= −

y

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

-2-

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Answers to 3.12 Systems

1) No solution 2) No solution 3) No solution 4) (−4, −1)5) (−4, −2) 6) (−1, 1) 7) (2, 4) 8) (3, 3)9) (−4, −1) 10) (−2, 2)