x

y

1st Quadrant2nd Quadrant

3rd Quadrant 4th Quadrant

13.1 – The Rectangular Coordinate System

origin

x-axis

y-axis

Coordinates of points: ,x y

Each point in the rectangular coordinate system has a unique set of coordinates.

The x coordinate is always first and the y coordinate is always second.

2,3

4, 1 3,0

13.1 – The Rectangular Coordinate System

x

y

1st Quadrant2nd Quadrant

3rd Quadrant 4th Quadrant

,x y ,x y

,x y ,x y

13.1 – The Rectangular Coordinate System

X

Y

AB

C

D

EF

GH

IJ

KM

A

D

B C

E F

G

H

I

J

K

M

L

4,3 2,2 4,4

2, 3 0,0 3,0

0,4

2,3

4,0

2,0

4, 2

0, 2

3, 3

L

1st 1st

2nd

2nd

3rd

4th

4th

x-axis

x-axis

x-axis

y-axis

y-axis

origin

0,4

Calculating Ordered Pairs and Graphing Linear Equations

13.2 – Graphing Linear Equations

2 8x y

x y

0

3

-4

2,3

4,6

4

2

6

0 2 8y

2 8y

4y

32 8x

6 8x

2x

24 8y

2 12y

6y

0,4

Calculating Ordered Pairs and Graphing Linear Equations

2 8x y

2,3

4,6

13.2 – Graphing Linear Equations

3,6

Calculating Ordered Pairs

2y x

x y

-3

0

10

0,0

5,10

6

0

5

32y

6y

0 2x

0 x

10 2x

5 x

13.2 – Graphing Linear Equations

Calculating Ordered Pairs and Graphing Linear Equations

2y x

3,6

0,0

5,10

13.2 – Graphing Linear Equations

9,2

Calculating Ordered Pairs

11

3y x

x y

9

0

1

0, 1

6,1

2

1

6 0

11

3y

11

13x 9

11

3y

3 1y

2y

1y

12

3x

6 x

13.2 – Graphing Linear Equations

Calculating Ordered Pairs and Graphing Linear Equations

11

3y x

9,2

0, 1

6,1

13.2 – Graphing Linear Equations

Identifying Intercepts

X

Y

X

Y

0,3

2,0 4,0

0, 2

X-intercept

Y-intercept

Y-intercept

X-intercept

13.3 – Intercepts

X

Y

X

Y

Identifying Intercepts

0,1

3,0 2,0

0,1

X-interceptX-intercept

Y-interceptY-intercept

13.3 – Intercepts

X

Y

X

Y

Identifying Intercepts

5,0

0, 4

0,0

X-intercept

X-intercept

Y-intercept

Y-intercept

13.3 – Intercepts

Calculating Intercepts

2 4x y

To find the x-intercepts, set y = 0 and solve for x

To find the y-intercepts, set x = 0 and solve for y

x-intercept: y = 0

2 0 4x

2x

y-intercept: x = 0

2 0 4y 4y

2,0 0, 4

2 4x

13.3 – Intercepts

Calculating Intercepts

To find the x-intercepts, set y = 0 and solve for x

To find the y-intercepts, set x = 0 and solve for y

2 3 6 0x y

x-intercept: y = 0

3x

y-intercept: x = 0

2y

3,0 0,2

2 3 0 6 0x 2 0 3 6 0y

2 6 0x 2 6x

3 6 0y

3 6y

13.3 – Intercepts

X

Y

Graphing Vertical and Horizontal Lines

3x

x y

23

1

5

3

3

13.3 – Intercepts

X

Y

Graphing Vertical and Horizontal Lines

4x

x y

54

0

3

4

4

13.3 – Intercepts

X

Y

Graphing Vertical and Horizontal Lines

1y

x y

14

1

1

1

3

13.3 – Intercepts

X

Y

Graphing Vertical and Horizontal Lines

3y

x y

35

3

3

1

1

13.3 – Intercepts