1 Math Pacing Graphing Linear Equations

Equations as Relations A linear equation can be written in the standard form of a linear equation: Ax + By = C, where A ≥ 0, A and B are not both zero, and A, B and C are integers whose greatest common factor is 1.

Example 5-1a Determine whether is a linear equation. If so, write the equation in standard form. First rewrite the equation so that the variables are on the same side of the equation. Simplify. Subtract z from each side. Original equation Since has 3 different variables, it cannot be written in the form Answer: This is not a linear equation. Identify Linear Equations

Example 5-1b Rewrite the equation so that both variables are on the same side. Determine whether is a linear equation. If so, write the equation in standard form. Original equation Subtract y from each side. Simplify. Identify Linear Equations

Example 5-1b To write the equation with integer coefficients, multiply each term by 4. Original equation Multiply each side of the equation by 4. Simplify. The equation is now in standard form where Answer: This is a linear equation. Identify Linear Equations

Answer: The equation is now in standard form where Example 5-1c Since the GCF of 3, 6, and 27 is not 1, the equation is not written in standard form. Divide each side by the GCF. Determine whether is a linear equation. If so, write the equation in standard form. Original equation Factor the GCF. Divide each side by 3. Simplify. Identify Linear Equations

Example 5-1d To write the equation with integer coefficients, multiply each term by 4. Determine whether is a linear equation. If so, write the equation in standard form. Original equation Multiply each side of the equation by 4. Simplify. Identify Linear Equations Answer: The equationcan be written as Therefore, it is a linear equation in standard form where

Example 5-1e Determine whether each equation is a linear equation. If so, write the equation in standard form. a. b. c. d. Answer: not a linear equation Answer: linear equation; Identify Linear Equations Answer: linear equation; 4x – y = 5

Graphing Linear Equations Equations as Relations The graph of a linear equation is a line. The line represents all the solutions of the linear equation. Also, every ordered pair on this line satisfies the equation.

Example 5-2a Graph In order to find values for y more easily, solve the equation for y. Original equation Add x to each side. Simplify. Graph by Making a Table

Example 5-2a Select five values for the domain and make a table. Then graph the ordered pairs. Multiply each side by 2. Simplify. (3, 8) 83 (2, 6) 62 (0, 2) 20 (–1, 0) 0–1 (–3, –4) –4–3 (x, y)(x, y) yx Graph by Making a Table

Example 5-2a Answer: When you graph the ordered pairs, a pattern begins to form. The domain of is the set of all real numbers, so there are an infinite number of solutions of the equation. Draw a line through the points. This line represents all the solutions of. Graph by Making a Table

Example 5-2b Answer:. Graph by Making a Table