1. Graphing in the Coordinate Plane
Chapter 10
Graphing in the Coordinate Plane

2. What You’ll learn To graph points on a plane
10-1 Graphing Points
What You’ll learn
To graph points on a plane

3. Rene Descartes develops Coordinate System
Coordinate Plane is a grid formed by a horizontal number line called the X axis and a vertical number line called the Y axis
Ordered Pair (x,y) gives the coordinates of the location of a point
X-coordinate is the first number of horizontal units from the origin
Y-coordinate is the second number of vertical units for the origin
-1,1
X axis
Y axis
origin
Ordered pair

4. The X and Y axes divide the coordinate plane into 4 QuadrantsII I
III IV

5. Writing Coordinates
The smiley face is 2 units to the right of the y axis, so the x coordinate is 2
The smiley face is 2 units above the x axis, so the y coordinate is 2
The ordered pair for the location of the fly is (2,2)

6. Graph point A (3,-5)
Text page

7. Horizontal and Vertical Lines
In a coordinate plane:
lines that are parallel to the x-axis are horizontal
Lines that are parallel to the y-axis are vertical
Assign Pr 10-1

8. 10-2 Graphing Linear Equations
What You’ll Learn:
To find ordered pairs that are solutions of linear equations
To graph linear equations

9. Determine whether each ordered pair is a solution of y = x + 5
(40,45)
y = x + 5
45 =
45 = 45
(21,27)
y = x + 5
27 =
27 = 26
Substitute for x and y in the equation

10. Determine whether each ordered pair is a solution of y = 3x - 1
(4, 11)
(7, 12)
(17, 23)
Text page 529 # 1-8; 32-37

11. Making a Table of Values y = x + 1 to graph a line
(x,y) -4
-4 + 1 -3
-4,-3 -2
-2 + 1 -1
-2,-1
0 + 1 1
0,1
1 + 1 2
1,2 3
3 + 1 4
3,4
Solutions of the equation
Graph points, draw line
Choose values for x

12. Using the graph find 2 more solutions of y = ½ x - 2
Graph the linear equation y = ½ x-2
How many solutions does a linear equation have??
Text page 529 # 9-28; pr 10-2

13. Graph each linear equation
2y + 10 = 2x
Does anyone remember how?
Slope Intercept Form?
y = mx + b

14. Practice
Graph y – 2 = ¼ x
Graph y = 5/6x + 3
Graph 2x + 3y = -6

15. 10-3 Finding the Slope of a line
What You’ll Learn:
To find and use the slope of a line
Investigation text page 533

16. Slope of a line
Slope is a ration that describes the steepness of a line
Slope = rise
run
Rise – compares the vertical change a line
Run – the horizontal change of a line

17. Finding Slope
Negative Slope
Positive slope

18. Finding Slope Slope = rise / run -6 6/-6 1/-1 or -1 +6
Pr 10-3; page 538 practice quiz, quiz 10-1 to 10-3

19. 10-4 Exploring Nonlinear Relationships
What You’ll Learn:
To graph nonlinear equations

20. Equations Linear Equations Nonlinear Equations
Represented by a straight line
Nonlinear Equations
Represented by a nonstraight line
y = x2 is an example of a curve called a parabola

21. Graphing a Parabola: Graph y = -x2 using integer values of x from –3 to 3
Make values of table x
-x2 y
(x,y) -3
-(-3)2 -9
-3,-9 -2
-(-2)2 -4
-2,-4 -1
-(-1)2
-1,-1
-(0)2
0,0 1
-(1)2
1,-1 2
-(2)2
2,-4 3
-(3)2
3,-9
Graph ordered pairs, then connect

22. Graph a Parabola Graph y = 2x2 using integer values of x from –3 to 3
Why is the graph of y = 2x2 only in Quadrants I and II?
Is (-1,-2) a solution??
10-4 a, b

23. Graph absolute value equations (V shape) : y = /x/
(x,y) -2
/-2/ 2
-2,2 -1
/-1/ 1
-1,-1
/0/
0,0
/1/
1,1
/2/
2,2

24. V Shape Equations Graph y = 2 /x/ using integers –2 to 2
Determine whether (4, 8) is a solution
Text page 542 # 1-24;10-4 c,d; pr 10-4

25. What You’ll learn: To graph translations

26. Graphing Translations
A transformation is a change of the position, shape, or size of a figure.
There are 3 types of transformations:
Translation: slide, flips, and turns
Move every point of a figure in the same direction and distance
Image
The end result after a transformation
Prime rotation
Used to identify and image point A` as prime A

27. Translating a Point
Translate F(4,1) up 2 units and 3 units to the left’ what are the coordinates of the image F’??
To translate use arrow notation F(4,1) F’(1,3)

28. Practice

29. Translating a Figures To translate a geometric figure
Translate each vertex (point) of the figure
Connect the image points to finish
The translated image should be the same dimensions as the original image

30. Translate ABC: right 2 units, down 2
A( )>>A’( )
B( )>>B’( )
C( )>>C’ ( )
Text page ; Pr 10-6
Write a rule for the translation using arrow notation

31. Write a Rule of Translation for MNP

32. 10-7 Symmetry and Reflections
What You’ll Learn:
To identify lines of symmetry
To graph reflections

33. Identify Symmetry
A line of symmetry can e drawn through the figure so that one side is a mirror image of the other
2 lines of symmetry
1 line of symmetry

34. Reflections
A reflection is a transformation that flips a figure over a line called line of reflection
When a figure is reflected the image is congruent to the original image

35. Graphing Reflections 3,1 Y reflection Original -1,3 1,3 -3,1 1,1 -1,1
Text page 556 #1-18; 27-30; pr 10-7
-1,-1
1,-1
3,-1
-3,-1
X reflection
X – Y reflection
1,-3
-1,-3

36. Lets Write the Rules for Reflections
Over the Y Axis
(X,Y) ( X , Y)
Over the X Axis
Over the Y and X Axis

37. 10-8 Rotations What you’ll Learn: To identify Rotational Symmetry
To rotate a figure about a point

38. Rotation
Rotation is a transformation that turns a figure about a fixed point called the center of rotation
Rotation of symmetry is if a figure can be rotated 180 degrees or less and match the original image
Rotations are made counter clockwise
A` for 90 degrees
A`` for 180 degrees
A``` for 270 degrees

39. Do the following figures have rotational symmetry ??
Text page 561 # 1-6
Angle of Rotation: 360 / 5 = 72

40. Angle of Rotation

41. “Image rotation”
360 90 90 90 90
270
180

42. “Image rotation” 360 90 90 90 90 270 180 original
Pr 10-8; re 10-1 to 10-4; 10-6 to 10-8, chapter test
270
180
original