1

2

4

5

7

2 2

Objective - To graph linear equations using x-y charts.

One Variable Equations Two Variable Equations2x - 3 = 11

+3 +3

2x = 14

x = 7

One Solution

x2 16=x = =−4 4 or x

Two Solutions

x + y = 5

Solutions:x = 1, y = 4

x = 2, y = 3

x = 4, y = 1

x = 5, y = 0

x = 7, y = -2

x y= =12

412

,

OrderedPairs (x,y)

(1,4)

(2,3)

(4,1)

(5,0)

(7,-2)

12

,4 12

⎛⎝⎜

⎞⎠⎟

x y

4

3

1

0

-21

24

1

2

Infinite Solutions

Determine whether the ordered pair is a solutionto the given equation.

2) x 8 y ; (12, 4)= − −

1) x y 5 ; (8,3)+ =−

4) y 3 x 1 ; (5,1)− = +

3) y 13 x ; ( 7,6)= + −

Not a solution

It is a solution

It is a solution

Not a solution

?8 3 5+ =−8 3 5+ ≠−

?12 8 4= −−12 8 4= + +

?6 13 7= +−6 13 7= −

?1 3 5 1− = +2 6− ≠

State whether the given point is a solution to 3x - y = 5.

1) (2, 1)

2) (4, 5)

3) (-3, -14)

4)

5) (-1, 2)

12

,−312

⎛⎝⎜

⎞⎠⎟

3(2) - 1 = 5 Yes

3(4) - 5 = 5 No

3(-3) - -14 = 5 Yes

Yes

3(-1) - 2 = 5 No 3 1

2⎛⎝⎜

⎞⎠⎟−−31

2=5

Complete the chart and graph.

y = 2x - 3x y

-3-2-1 0 1 2 3

2(-3) - 3 = -92(-2) - 3 = -7-5-3-113

x

y

x

yComplete the chart and graph.

y = 2x - 3x y

-3-2-1 0 1 2 3

2(-3) - 3 = -92(-2) - 3 = -7-5-3-113

x

yComplete the chart and graph.

y = 2x - 3x y

-3-2-1 0 1 2 3

2(-3) - 3 = -92(-2) - 3 = -7-5-3-113

x

yComplete the chart and graph.

y = 2x - 3x y

-3-2-1 0 1 2 3

2(-3) - 3 = -92(-2) - 3 = -7-5-3-113

x

yComplete the chart and graph.

y = 2x - 3x y

-3-2-1 0 1 2 3

2(-3) - 3 = -92(-2) - 3 = -7-5-3-113

x

yComplete the chart and graph.

y = 2x - 3x y

-3-2-1 0 1 2 3

2(-3) - 3 = -92(-2) - 3 = -7-5-3-113

This line represents allreal solutions to y = 2x - 3.

2 72

⎛⎝⎜

⎞⎠⎟−3 4=

72

1) 2x + y = 5 2) -x + 2y = -4-2x -2x

y = -2x + 5

+x +x2y = x - 42 2

yx

=−42

y x= −12

2

yx

= +−

242

Solve the following equations for y. (Function Form)

3) 3x + 5y = 10 4) -2x + 3y = -6-3x -3x

5y = -3x + 105 5

3x 10y5

− +=

+2x +2x

3x 10y5 5

−= +

3y x 25

=− +

3y = 2x - 63 3

2x 6y3 3

−= +

2y x 23

= −

2x 6y3−=

Solve the following equations for y. (Function Form)

x

y

Solve the equation for y, complete the chart, and graph.

1) 3x + 2y = 4-3x -3x

2y = -3x + 42 2

3x 4y2

− +=

3x 4y2 2

−= +

3y x 22

=− +

x y

-4

-2

0

2

4

6

8

5

2

-1

-4

-7

x

y2) x - 3y = 6

-x -x

-3y = -x + 6-3 -3

x 6y3

− +=−x 6y3 3

−= +− −1y x 23

= −

x y

-6

-3

0

3

6

9

-4

-3

-2

-1

0

1

Solve the equation for y, complete the chart, and graph.

x

y

Solve the equation for y, find at least five solutions, and graph.

3) x + 2y = 8-x -x

2y = -x + 82 2

x 8y2

− +=

x 8y2 2−= +

1y x 42

=− +

x y

-4

-2

0

2

4

6

6

5

4

3

2

1