1. 2.2 Graphs of Equations in Two Variables Chapter 2 Section 2: Graphs of Equations in Two Variables In this section, we will… Determine if a given ordered pair satisfies a graph Find the intercepts of a graph of a function algebraically and graphically Identify symmetries given a graph or equation

2. 2.2 Determine if a Given Ordered Pair Satisfies a Graph Example: Determine if the given points are on the graph of the equation.

3. 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically Example: Find the intercepts and graph of using a table of values. The y-intercept is where x = 0, and the x-intercept is where y = 0. Label the intercepts. x y x-intercept y-intercept

4. 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically Example: Find the intercepts and graph of using a table of values. Label the intercepts. x y x-intercept y-intercept

5. 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically Example: Find the intercepts and graph of using a table of values. Label the intercepts. x y x-intercept(s) y-intercept

6. 2.2 Find the Intercepts of a Graph of a Function Algebraically and Graphically Example: Find the intercepts and graph of using a table of values. Label the intercepts. x y x-intercept(s) y-intercept

7. 2.2 Identify Symmetries Given a Graph or Equation A graph is said to be symmetric with respect to the x-axis if, for every point (x, y) on the graph, the point (x, -y) is also on the graph. Example: Draw a complete graph so that it is symmetric with respect to the x-axis. If you replace y with –y in the equation and an equivalent equation results, the graph is symmetric with respect to the x-axis.

8. 2.2 Identify Symmetries Given a Graph or Equation A graph is said to be symmetric with respect to the y-axis if, for every point (x, y) on the graph, the point (-x, y) is also on the graph. Example: Draw a complete graph so that it is symmetric with respect to the y-axis. If you replace x with –x in the equation and an equivalent equation results, the graph is symmetric with respect to the y-axis.

9. 2.2 Identify Symmetries Given a Graph or Equation A graph is said to be symmetric with respect to the origin if, for every point (x, y) on the graph, the point (-x, -y) is also on the graph. Example: Draw a complete graph so that it is symmetric with respect to the origin. If you replace x with –x and y with –y in the equation and an equivalent equation results, the graph is symmetric with respect to the origin.

10. 2.2 Identify Symmetries Given a Graph or Equation Example: For each of the graphs below, find the intercepts and indicate if the graph is symmetric with respect to the x-axis, the y-axis or the origin. x-intercept(s): y-intercept(s): symmetries: x-intercept(s): y-intercept(s): symmetries:

11. 2.2 Identify Symmetries Given a Graph or Equation Example: For each of the graphs below, find the intercepts and indicate if the graph is symmetric with respect to the x-axis, the y-axis or the origin. x-intercept(s): y-intercept(s): symmetries: x-intercept(s): y-intercept(s): symmetries:

12. 2.2 Identify Symmetries Given a Graph or Equation Example: Find the intercepts and test for symmetry of x-intercept(s): y-intercept(s): Symmetry with respect to the: x-axisy-axisorigin

13. 2.2 Identify Symmetries Given a Graph or Equation Example: Find the intercepts and test for symmetry of x-intercept(s): y-intercept(s): Symmetry with respect to the: x-axisy-axisorigin

14. 2.2 Identify Symmetries Given a Graph or Equation Example: Find the intercepts and test for symmetry of x-intercept(s): y-intercept(s): Symmetry with respect to the: x-axisy-axisorigin