The symmetry with respect to both axes and the origin for the equation, y = − 3 x + 7 . Also sketch the graph of the equation. The equation, y = − 3 x + 7 , is not symmetric about the x -axis, the y -axis, and the origin. Explanation: Consider the equation, y = − 3 x + 7 . To check for symmetry about y -axis, replace x with − x in the original equation, and simplify the equation. If the equation after simplifying is equivalent to the original equation, then the given equation will be symmetric about y -axis. Replace x with − x in the original equation as, y = − 3 − x + 7 = 3 x + 7 Since the new equation is not equivalent to the original equation, the given equation is not symmetric about y -axis. To check for symmetry about x -axis, replace y with − y in the original equation, and simplify the equation. If the equation after simplifying is equivalent to the original equation, then the given equation will be symmetric about x -axis. Replace y with − y in the original equation − y = − 3 x + 7 y = 3 x − 7 Since the new equation is not equivalent to the original equation, the given equation is not symmetric about x -axis. To check for symmetry about the origin, replace x with − x , and y with − y in the original equation, and simplify the equation. If the equation after simplifying is equivalent to the original equation, then the given equation will be symmetric about the origin. Replace x with − x and y with − y in the original equation as, − y = − 3 − x + 7 − y = 3 x + 7 y = − 3 x − 7 Since the new equation is not equivalent to the original equation, the given equation is not symmetric about the origin. Plot the graph of the equation, y = − 3 x + 7 , by using the table below which consists of the different values of y for the different values of x . y = − 3 x + 7 16 13 7 1 − 5 x − 3 − 2 0 2 4 Now plot the points,
The symmetry with respect to both axes and the origin for the equation, y = − 3 x + 7 . Also sketch the graph of the equation. The equation, y = − 3 x + 7 , is not symmetric about the x -axis, the y -axis, and the origin. Explanation: Consider the equation, y = − 3 x + 7 . To check for symmetry about y -axis, replace x with − x in the original equation, and simplify the equation. If the equation after simplifying is equivalent to the original equation, then the given equation will be symmetric about y -axis. Replace x with − x in the original equation as, y = − 3 − x + 7 = 3 x + 7 Since the new equation is not equivalent to the original equation, the given equation is not symmetric about y -axis. To check for symmetry about x -axis, replace y with − y in the original equation, and simplify the equation. If the equation after simplifying is equivalent to the original equation, then the given equation will be symmetric about x -axis. Replace y with − y in the original equation − y = − 3 x + 7 y = 3 x − 7 Since the new equation is not equivalent to the original equation, the given equation is not symmetric about x -axis. To check for symmetry about the origin, replace x with − x , and y with − y in the original equation, and simplify the equation. If the equation after simplifying is equivalent to the original equation, then the given equation will be symmetric about the origin. Replace x with − x and y with − y in the original equation as, − y = − 3 − x + 7 − y = 3 x + 7 y = − 3 x − 7 Since the new equation is not equivalent to the original equation, the given equation is not symmetric about the origin. Plot the graph of the equation, y = − 3 x + 7 , by using the table below which consists of the different values of y for the different values of x . y = − 3 x + 7 16 13 7 1 − 5 x − 3 − 2 0 2 4 Now plot the points,
Solution Summary: The author explains that the equation, y=-3x+7, is not symmetric about both axes and the origin.
How do you find the axis of symmetry? *
Your answer
What do you call the point that the axis of symmetry crosses through? *
Your answer
CLASSWORK (Suggested time: 15 minutes)
For the equation y = 2x + 3:
a) Complete the table of ordered pairs below.
8.
-4
-3
<-2
-1
1.
b) Plot the above co-ordinate points on the Cartesian plane. Join points to form a graré
c) Write down the verbal representation of the equation.
=56 (x+
2. Study the graph below:
110 (x
rrection
the
(xt
%3D
ult
SS
a) Complete the table of ordered pairs for the graph above.
-3
-2
-1
1
4
-4
y
b) Write down the equation of the graph.
c) Write down the verbal representation of the equation.
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FUNCTIONS AND RELATIONSHIPS: EQUIVALENT FORMS (Lesson 4)
(Draft)
Grade 9 Lesson Plan: 1+4 Intervention-Term 3
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basic education
EPUBLIC OF SOUTH AFRICA
3.