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Graphing in the
Coordinate Plane
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10-1 Graphing Points in Four Quadrants
Objective 1: Graphing Points on the Coordinate Plane
A coordinate plane is a grid formed by a horizontal number line called the _______ and a vertical
number line called the _________
An _______________(x,y) gives the coordinates of the location of a point.
The 1st number in an ordered pair is the ____________________. It tells the number of horizontal units
a point is from 0. The 2nd number is the _________________. It tells the number of vertical units a
point is from 0.
What are the coordinates of points A, B, and C? ______________________________
What are the coordinates of the origin? _______________
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The x- and y- axes divide the coordinate plane into four _________________
Graphing a point
Graph each point on the coordinate plane above: P(3, 5) ; Q(-3, -5) ; R(-3, 5)
In which quadrant is each point located?
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In the coordinate plane, lines that are parallel to the x-axis are horizontal and lines that are parallel to
the y-axis are vertical.
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10-2 Graphing Linear Equations
Determine whether each ordered pair is a solution of y = 3x – 1.
(4, 11) ______ (7, 12) ______ (17, 23)_____
You can find solutions of an equation by making a table. Choose different values for x and substitute
them into the equation.
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Find 3 solutions of each equation:
1) y = x – 2
______________________________________________________
2) y = x + 5
______________________________________________________
3) y = -3x
________________________________________________________
Objective 2: Graphing Linear Equations
The graph of an equation is the graph of all the points with coordinates that are solutions of the
equation. An equation is the linear equation when the graph of its solutions is in a line.
Using the graph, find 2 more solutions of y = x + 1 ________________________________
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10-3 Finding the Slope of a Line
Objective 1
Slope is a ratio that describes the steepness of a line. For any line, slope compares the vertical change,
called the rise, to the horizontal change, called the run.
When a line goes upward from left to right, it has a positive slope. When a line goes downward from
left to right, it has a negative slope.
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Graphing a Line
Draw a line through the origin with a slope of
3
−2
Step 1: Graph a point at (0,0)
Step 2: Move 3 units down and then 2 units to the right. Graph the second point.
Step 3: Connect the points to form a line
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10-4 Exploring Nonlinear Relationships
You know that the graph of a linear equation is a straight line. A nonlinear equation is an equation with
a graph that is not a straight line. The graph of the equation
y = −𝑥
2
is an example of a curve called a parabola. When you throw or kick a ball in the air, the path
the ball follows is a parabola.
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The equation y = |𝑥 | is an absolute value equation with 2 variable. The graphs of absolute value
equations are V-shaped.
𝐺𝑟𝑎𝑝ℎ 𝑦 = 2|𝑥 | 𝑢𝑠𝑖𝑛𝑔 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑥 𝑓𝑟𝑜𝑚 − 2 𝑡𝑜 2.
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10-6 & 10-7 & 10-8 Translations; Symmetry and Reflections; Rotations
A ______________________ is a change of the position, shape, or size of a figure. The figure you get
after a transformation is the ________ of the original. You use prime notation (A’) to identify an image
point. You read A’ as “A prime. If the point has been moved twice you’d read A” as “A double prime”. 3
types of transformations the change POSITION ONLY are :
1) Translation – slides
Moves every point of a figure the same distance and in the same
direction
2) Reflection – flip
Flips a figure over a line called the line of reflection. When reflected,
the image is congruent to the original.
3) Rotations – turns
Turns a figure about a fixed point called the center of rotation. This
year they will only be COUNTERCLOCKWISE
TranSLations -SLide
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ReFLections - FLip
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Symmetry
A figure has line symmetry if a line can be drawn through the figure so that one side is a mirror image of
the other. A line of symmetry divides a figure into mirror images.
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RoTation - Turn
A figure has rotational symmetry if can be rotated 180º or less and match the original figure. The figure
turns about a fixed point called the center of rotation. In this course, all rotations are
COUNTERCLOCKWISE!
When a figure has rotational symmetry, the angle measure that it rotates is the angle or rotation.
Does the wheel have rotational symmetry?
If so, what is the angle of rotation?
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Graphing Equations using TI-73
Plots – all off ( go to 2nd plot and hit 4)
Window

Xmin = -10

Xmax=10

Xscl=1
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Ymin=-10
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Ymax=10

Yscl=1
Tblset (2nd tblset)

Tblstart=-10

Tbl=1

Independent and Dependent = auto
Format (2nd format)

Coordinates on
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Grid off

Axes on
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Label off
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Expr on
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