2.2

an ordered pair that fits into the equation is a solution

• to determine if an ordered pair is a solution, plug it into each of the corresponding variables in the equation

you create ordered pairs by choosing a number to plug into a variable​ (usually x), then solving for the other variable (usually y).

• if you get a dependent variable that is imaginary or​ undefined, the dependent variable you chose is not in the domain of the equation

to solve a linear equation, you must

• move all terms to one side of the​ equation, leaving zero on the other side

  • to find the y-intercept, replace all of the x’s with zero

  • to find the x-intercept, replace all of the y’s with zero

• factor the quadratic (if necessary)

the three tests for symmetry algebraically:

• symmetry of the y-axis: replace x’s with -x’s. if the equation simplifies back to the original equation, there is symmetry about the y-axis

• symmetry of the x-axis: replace y’s with -y’s. if the equation simplifies back to the original equation, there is symmetry about the x-axis

• symmetry of the origin: replace both x and y’s with -x and y’s. if the equation simplifies back to the original equation, there is symmetry about the origin