The Slope of a Line 3.1 – Paired Data and The Rectangular Coordinate System
y
  x, y 
 x, y 
origin
y-axis
x
x-axis
  x,  y 
 x,  y 
3.1 – Paired Data and The Rectangular Coordinate System
Coordinates of points:
 x, y 
Also referred as an ordered pair.

The x coordinate is always first and
the y coordinate is always second.
Each point in the rectangular
coordinate system has a unique set
of coordinates.
3,0  4, 1  2,3

 4, 1
 2,3

3,0
3.1 – Paired Data and The Rectangular Coordinate System
Graphing Equations
y  2 x
x
y
 3,6
-3
 0, 0 
0
2

Y

X
-4

3.1 – Paired Data and The Rectangular Coordinate System
Graphing Equations
Y
x
y
-6
-2

3
6


X
3.1 – Paired Data and The Rectangular Coordinate System
Graphing Equations and Vertical Translations

Y

X

3.1 – Paired Data and The Rectangular Coordinate System
Graphing Equations and Vertical Translations
Y



X
3.1 – Paired Data and The Rectangular Coordinate System
Identifying Intercepts
Y
 0,3 
Y
Y-intercept

X-intercept
X-intercept
 2, 0 
 4, 0 

X
Y-intercept

 0, 2
X
3.1 – Paired Data and The Rectangular Coordinate System
Identifying Intercepts
Y
Y
Y-intercept
 0,1
Y-intercept
0,1



3,0
X-intercept
X


 2,0
X-intercept
X
3.1 – Paired Data and The Rectangular Coordinate System
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
2x  y  4
x-intercept: y = 0
y-intercept: x = 0
2x  0  4
2x  4
x2
2  0  y  4
y  4
 2, 0 
 0, 4
3.1 – Paired Data and The Rectangular Coordinate System
Identifying Intercepts and Graphing Equations
Y


 0, 4
 2, 0 
X
3.1 – Paired Data and The Rectangular Coordinate System
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
2x  3 y  6  0
x-intercept: y = 0
y-intercept: x = 0
2x  3 0  6  0
2  0  3 y  6  0
3y  6  0
2x  6  0
2x  6
x3
3,0
3y  6
y2
 0, 2 
3.1 – Paired Data and The Rectangular Coordinate System
Identifying Intercepts and Graphing Equations
Y
 0, 2  

3,0
X
3.1 – Paired Data and The Rectangular Coordinate System
Graphing Vertical and Horizontal Lines
x  3
x
y
3
2
3
1
3
5
Y
X
3.1 – Paired Data and The Rectangular Coordinate System
Graphing Vertical and Horizontal Lines
x4
x
y
4
5
4
0
4
3
Y
X
3.1 – Paired Data and The Rectangular Coordinate System
Graphing Vertical and Horizontal Lines
y 1
x
y
4
1
1
1
3
1
Y
X
3.1 – Paired Data and The Rectangular Coordinate System
Graphing Vertical and Horizontal Lines
y  3
x
y
5
3
1
3
1
3
Y
X
3.2 – The Slope of a Line
Slope is a rate of change.
Y


 x2 , y2 
 x1, y1 
X
3.2 – The Slope of a Line
Y


1,0
 4,5
X
3.2 – The Slope of a Line
 4,5
Y

 5,1

X
3.2 – The Slope of a Line
Slope of any Vertical Line
x2
Y

 2,3
X

undefined
 2, 4
3.2 – The Slope of a Line
Slope of any Horizontal Line
y  3
 3, 3

0
Y
X

 4, 3
3.2 – The Slope of a Line
Slopes of 5 lines are given below:
Parallel Lines ( // ): two or more lines with the same slope.
Which slopes represent parallel lines?
3.2 – The Slope of a Line
Slopes of 5 lines are given below:
The product of their slopes is –1.
The slopes of perpendicular lines are negative reciprocals of
each other.
Which slopes represent perpendicular lines?
3.2 – The Slope of a Line
What is the slope of a line that contains the following points?
What is the slope of a line that is parallel to this line?
What is the slope of a line that is perpendicular to this line?