4.2.1 Graphing Functions
Key Objectives • Find solutions to equations with two variables. • Check solutions of equations. • Read solutions for graphs. • Graph linear functions. Key Terms • A linear equation is an equation whose solutions form a straight line on a coordinate plane. An equation with two variables, such as x and y , can have an infinite number of solutions. Each solution is a pair of values that can be written as an ordered pair ( x , y ) and graphed on a coordinate plane. Example 1 Finding Solutions to Equations with Two Variables In Example 1, Prof. Burger finds four solutions to a given equation. He substitutes each of the four given x -values, 0, 1, 2, and 3, into the equation to find each corresponding y -value. He then writes these solutions as ordered pairs.
Example 2 Checking Solutions of Equations with Two Variables
To determine whether a given ordered pair is a solution of an equation, substitute the two values from the ordered pair into the equation for the variables and simplify. If the resulting statement is true, then the ordered pair is a solution to the equation. If the resulting statement is false, then the ordered pair is not a solution to the equation.
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