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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?
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