Equations in two variables can be represented by a graph. Each ordered pair (x,y) that makes the equation true is a point on the graph. Graph equation by plotting points and then connecting the points with smooth curves. Use curves except for linear equations 2.2 Graphs of Equations

Linear Example x y Create a table of points: xy=-5x

Nonlinear Example x y Create a table of points: x

Intercepts Where the graph crosses the axes x-intercept: cross the x-axis => y-intercept: cross the y-axis =>

Int Example 1 Find the intercepts for the following equation. y-intercepts: x-intercepts:

Int Example 2 Find the intercepts for the following equation. y-intercepts: x-intercepts: y-intercepts:

Symmetry If the graph has a mirror-image over x-axis, y-axis, or origin. y-axis symmetry: symmetry over the y-axis(x=0) x-axis symmetry: symmetry over the x-axis(y=0) If replacing -x for x doesn’t change the equation => y-axis symmetry If replacing -y for y doesn’t change the equation => x-axis symmetry

Symmetry origin symmetry: symmetry over the origin (0, 0) If replacing -x for x and -y for y doesn’t change the equation => origin symmetry

Example 1 Try y-axis symmetry: -x for x Try x-axis symmetry: -y for y Try origin symmetry: -x for x, -y for y

Example 2 Try y-axis symmetry: -x for x Try x-axis symmetry: -y for y Try origin symmetry: -x for x, -y for y