x

y

1st Quadrant2nd Quadrant

3rd Quadrant 4th Quadrant

origin

x-axis

y-axis

,x y ,x y

,x y ,x y

3.1 – Paired Data and The Rectangular Coordinate System

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

3.1 – Paired Data and The Rectangular Coordinate System

Also referred as an ordered pair.

3,0 2,3 4, 1

Graphing Equations

2y x

3,6

0,0

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

x y

-3

0

2

 

 

 

-4

Graphing Equations

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

x y

-6

3

6

 

 

 

 

 

 -2

Graphing Equations and Vertical Translations

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

 

 

 

Graphing Equations and Vertical Translations

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

 

 

 

Identifying Intercepts

X

Y

X

Y

0,3

2,0 4,0

0, 2

X-intercept

Y-intercept

Y-intercept

X-intercept

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

X

Y

Identifying Intercepts

0,1

3,0 2,0

0,1

X-interceptX-intercept

Y-interceptY-intercept

3.1 – Paired Data and The Rectangular Coordinate System

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

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

Identifying Intercepts and Graphing Equations

3.1 – Paired Data and The Rectangular Coordinate System

 

2,0

0, 4

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

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

Identifying Intercepts and Graphing Equations

3.1 – Paired Data and The Rectangular Coordinate System

 

3,0

0,2

X

Y

Graphing Vertical and Horizontal Lines

3x

x y

23

1

5

3

3

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

Graphing Vertical and Horizontal Lines

4x

x y

54

0

3

4

4

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

Graphing Vertical and Horizontal Lines

1y

x y

14

1

1

1

3

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

Graphing Vertical and Horizontal Lines

3y

x y

35

3

3

1

1

3.1 – Paired Data and The Rectangular Coordinate System

X

Y

Slope is a rate of change.

2 2,x y

1 1,x y

3.2 – The Slope of a Line

 

 

 

X

Y

1,0

4,5

3.2 – The Slope of a Line

 

 

 

 

X

Y

5,1

4,5

3.2 – The Slope of a Line

 

 

 

 

X

Y

2, 4

2,3

undefined

Slope of any Vertical Line 2x

3.2 – The Slope of a Line

 

 

 

 

X

Y

3, 3

4, 3

0

Slope of any Horizontal Line 3y

3.2 – The Slope of a Line

 

 

 

 

3.2 – The Slope of a Line

Parallel Lines ( // ): two or more lines with the same slope.

Which slopes represent parallel lines?

 

Slopes of 5 lines are given below:

   

3.2 – The Slope of a Line

 

The product of their slopes is –1.

The slopes of perpendicular lines are negative reciprocals of each other.

 

Slopes of 5 lines are given below:

   

Which slopes represent perpendicular lines? 

 

3.2 – The Slope of a Line

What is the slope of a line that is parallel to this line?

 

What is the slope of a line that contains the following points?

   

 

What is the slope of a line that is perpendicular to this line?