supplemental worksheet problems to accompany: the algebra 2

© 2008 Jason Gibson / MathTutorDVD.com The Algebra 2 Tutor Section 1 – Graphing Equations

Supplemental Worksheet Problems To Accompany:

The Algebra 2 Tutor

Section 1 – Graphing Equations

Please watch Section 1 of this DVD before working these problems.

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1) Plot the point below on an x-y coordinate axis.

( )5, 2


( )1, 3−



( )3,2−


( )4,5−



12,2

⎛ ⎞− −⎜ ⎟⎝ ⎠


3 1,2 2

⎛ ⎞−⎜ ⎟⎝ ⎠


7) Complete the table of values for the equation below then graph the equation using the points.

4y x= − x y

54-1



2xy =

x y

1-1-4



3 1y x= +

x y -2

0

1


10) Graph the equation by using the intercept method.

7x y+ =



2x y− = −



3 1x y+ = −



3 2x y 6− =


Question

Answer


( )5, 2

Begin.

We start by drawing the x-y coordinate axes.

Since our point is (5,2), we move along the x-axis 5 units, then move up the y-axis by 2 units. This is our point. Ans: See graph at left.

x

y

x

y

x

y

x

y

(5,2)


Question

Answer


( )1, 3−

Begin.


Since our point is (1,-3), we move along the x-axis 1 units, then move down the y-axis by 3 units. This is our point. Ans: See graph at left.

x

y

x

y

x

y

x

y

(1,-3)


Question

Answer


( )3,2−

Begin.


Since our point is (-3,2), we move to the left along the x-axis 3 units, then move up the y-axis by 2 units. This is our point. Ans: See graph at left.

x

y

x

y

x

y

x

y

(-3,2)


Question

Answer


( )4,5−

Begin.


Since our point is (-4,5), we move to the left along the x-axis 4 units, then move up the y-axis by 5 units. This is our point. Ans: See graph at left.

x

y

x

y

x

y

x

y

(-4,5)


Question

Answer


12,2

⎛ ⎞− −⎜ ⎟⎝ ⎠

Begin.


Since our point is (-2, -1/2), we move to the left along the x-axis 2 units, then move down the y-axis by ½ of a unit. This is our point. Ans: See graph at left.

x

y

x

y

x

y

x

y

(-2, -1/2)


Question

Answer


3 1,2 2

⎛ ⎞−⎜ ⎟⎝ ⎠

Begin.


Since our point is (3/2, -1/2), we move to the right along the x-axis by 3/2 units (note that 3/2 = 1.5), then move down the y-axis by ½ of a unit. This is our point. Ans: See graph at left.

x

y

x

y

x

y

x

y

(3/2, -1/2)


Question

Answer


4y x= −

Begin.

Plug in x = 5...

5 41

yy= −=

We need to plug the values of ‘x’ into the equation and solve for the corresponding values of ‘y’. We do this for the first point and find the corresponding value for ‘y’.

Plug in x = 4...

4 40

yy= −=

We need to plug the values of ‘x’ into the equation and solve for the corresponding values of ‘y’. We do this for the second point and find the corresponding value for ‘y’.

Plug in x = -1...

1 45

yy= − −= −

We need to plug the values of ‘x’ into the equation and solve for the corresponding values of ‘y’. We do this for the third point and find the corresponding value for ‘y’. (continued on next page).

x y 54-1


Put the calculated values for ‘y’ into the table.

Now we need to plot the points. For each point, we travel along ‘x’ by the amount given in the ‘x’ column, then travel up or down in the ‘y’ column as shown in the table. We put a dot for each point. After you have plotted the points, draw a straight line through them. Ans: See graph at left.

x y 54-1

10-5

x

y

x

y

(5, 1)

(4, 0)

(-1, -5)


Question

Answer


2xy =

Begin.

Plug in x = 1...

12

y =

We need to plug the values of ‘x’ into the equation and solve for the corresponding values of ‘y’. We do this for the first point and find the corresponding value for ‘y’.

Plug in x = -1...

12

y = −


Plug in x = -4...

422

y

y

= −

= −


x y 1-1-4



Put the calculated values for ‘y’ into the table.

x y 1

-1

-4

½

- ½

-2

Now we need to plot the points. For each point, we travel along ‘x’ by the amount given in the ‘x’ column, then travel up or down in the ‘y’ column as shown in the table. We put a dot for each point.

After you have plotted the points, draw a straight line through them.

Ans: See graph at left.

x

y

x

y

(1, 1/2)(-1, -1/2)

(-4, -2)

Page 21


Question Answer


Begin.

3 1y x= +

x y -2

0

1

orresponding alues of ‘y’.

int and find the corresponding value for ‘y’.

We need to plug the values of ‘x’ into the equation and solve for the cv We do this for the first po( )

Plug in x = -2...

3 2 16 15

yyy

= − +

= − += −


( )

Plug in = 0...

3 0 10 11

yyy

= +

= +=

x


( )

Plug in x = 1...

3 1 13 14

yyy

= +

= +=


Put the calculated values for ‘y’ into the

ble.

ta

x y -2 -5

0

1

1

4

Now we need to plot the points. For each point, we travel along ‘x’ by the amount given in the ‘x’ column, then travel up or down in the ‘y’ column as shown in the table. We put a dot for each point.

After you have plotted the points, draw a straight line through them. Ans: See graph at left.

x

y

x

y

(1, 4)

(0, 1)

(-2, -5)


Question

Answer

10) Graph the equation by using the intercept method. Begin.

7x y+ =

Substitute y=0 and calculate ‘x’.

0 and alculate ‘y’.

Plug in = 0...

0 77

x yy

y

+ =+ ==

x

7

Any line is completely defined by two points. We can easily find two points onany line by: - Substitute x=0 and calculate ‘y’. - We begin by substituting x=c

( )0, 7

We write down the point that we found in the previous step. This is called the y-intercept, because it is the point where the line intercepts the y-axis.

Plug in y = 0...

70 77

x yxx

+ =+ ==

We now substitute y=0 and calculate the corresponding ‘x’ value.

( )7,0

Write down the point that we found in the previous step. This is called the x-intercept, because it is the point where the line intercepts the x-axis. (continued on next page)


Question

Answer

two intercept points that we have found and draw a line through them.

Ans: See graph at left.

Plot the

x

y

x

y

(0, 7)

(7, 0)


Question

Answer


2x y− = −

Begin.

Any line is completely defined by two points. We can easily find two points on any line by: - Substitute x=0 and calculate ‘y’. - Substitute y=0 and calculate ‘x’. We begin by substituting x=0 and calculate ‘y’.

Plug in = 0...

20 2

22

x yy

yy

− =− =

− = −=

x

−−


( )0, 2


Plug in y = 0...

20 2

2

x yxx

− = −− = −= −


( )2,0−


Question

Answer

two intercept points that we have found and draw a line through them. Ans: See graph at left.

Plot the

yy

(0, 2)(-2, 0)

xx


Question

Answer


3 1x y+ = −

Begin.


( )

Plug in = 0...

3 13 0 1

1

x yy

y

+ = −

+ = −

= −

x


( )0, 1 −

Plug in y = 0...

3 13 0 13 1

13

x yxx

x

+ = −+ = −= −

= −


1 ,03

⎛ ⎞−⎜ ⎟⎝ ⎠



Question

Answer


Plot the

yy

(-1/3,0)

xx

(0, -1)


Question

Answer


63 2x y− =

Begin.


( )

Plug in = 0...

3 2 63 0 2 6

2 63

x yy

yy

− =

− =

− == −

x


( )0, 3 −


( )

Plug in y = 0...

3 2 63 2 0 63 6

2

x yxx

x

− =

− =

==


( )2,0


Question

Answer


Plot the

yy

xx(2, 0)

(0,-3)

supplemental worksheet problems to accompany: the algebra 2

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