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.
Summarize what you have learned from Graphing and Solving problems Involving circles and other geometric figures. Use graphing to illustrate situation and solving problems involving circles and other geometric figures on the coordinate plane.
Part one: Graph the circle (x-2)squared + (y-1)squared=25
Submit a screenshot of your graphed circle.
Part two: For each point, determine if it is on the circle. If not, decide whether it is inside the circle or outside the circle
1. (4,0)
2. (-3,3)
3. (-2,-2)
Chapter 1 Solutions
Bundle: College Algebra, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's College Algebra, 10th Edition, Single-Term