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Math Pacing

Graphing Linear Equations. 1. Math Pacing. Graphing Linear Equations. 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.

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Math Pacing

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  1. Graphing Linear Equations 1 Math Pacing

  2. Graphing Linear Equations 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. Equations as Relations

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

  4. Determinewhether 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 Rewrite the equation so that both variables are on the same side.

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

  6. Determinewhether is a linear equation. If so,write the equation in standard form. Original equation Factor the GCF. Divide each side by 3. Simplify. Answer: The equation is now in standard form where Identify Linear Equations 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.

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

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

  9. Graphing Linear Equations 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. Equations as Relations

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

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

  12. When you graph the ordered pairs, a pattern begins to form. The domain ofis 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 5-2a Answer:

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

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