Graphs of Equations in Two Variables The solution of an equation is the set of all of the ordered pairs that make the equation true. Ex 1: Use a t-chart to graph: Ex 2: Use a t-chart to graph: Ex 3: Use a t-chart to graph:

Intercepts An x-intercept is a point where a graph of an equation intersects the x-axis. (a,0) An y-intercept is a point where a graph of an equation intersects the y-axis. (0,b) Ex 4: Find the intercepts of: y-intercept: (0,3); x-intercepts: (-3,0) and (1,0)

Equation of a Circle If a circle is centered at (h,k) with a radius of r, then the standard form of its equation is: Ex 5a: Graph: Ex 5b: Graph:

Ex 6a: Find the equation of a circle with center (-5,6) and a radius of 9. Ex 6b: Find the equation of a circle with a diameter with endpoints (-5,6) and (1,8). Ex 7: Rewrite this equation in standard form.

Symmetry To test for symmetry with respect to the x – axis, we check to see if the equation is unchanged when y is replaced by -y. To test for symmetry with respect to the y – axis, we check to see if the equation is unchanged when x is replaced by -x. To test for symmetry with respect to the origin, we check to see if the equation is unchanged when x is replaced by -x and y is replaced by -y.

Ex 8: Test the equation for symmetry and sketch: Symmetric with respect to the x-axis. Ex 9: Test the equation for symmetry and sketch: Symmetric with respect to the x-axis, y-axis, and origin.

Assignment S 2.2: pg 167 #7-10,12,16,17,28,34,40