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4-4 Equations as Relations Objectives 1. use an equation to determine the range for a given domain 2. graph the solution set for a given domain.

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Presentation on theme: "4-4 Equations as Relations Objectives 1. use an equation to determine the range for a given domain 2. graph the solution set for a given domain."— Presentation transcript:

1 4-4 Equations as Relations Objectives 1. use an equation to determine the range for a given domain 2. graph the solution set for a given domain

2 The equation p = 0.69d is an example of an equation in two variables. A solution of an equation in two variables is an ordered pair that results in a true statement when substituted into the equation.

3 List some pairs of numbers that will satisfy the equation x + y = 4. x = 1 and y = 3 x = 2 and y = 2 x = 4 and y = 0 What about negative numbers? If x = -1 then y = ? y = 5

4 x + y = 4 What about decimals? If x = 2.6 then y = ? y = 1.4 Now, lets graph the pairs of numbers we have listed.

5 (1, 3) (2, 2) (4, 0) (-1, 5) (2.6, 1.4) Connect the points on your graph. What does the graph look like?

6 It is a straight line! It is a linear relation. All solutions for theequation x+y=4! Is (3, -1) a solution to this equation? NO! You can check by graphing it or plugging into the equation! What does the line represent?

7 1) Which is a solution to 2x – y = 5? 1.(2, 1) 2.(3, 2) 3.(4, 3) 4.(5, 4) Answer Now

8 2) Which ordered pair is not a solution to the graph shown? 1.(0, -1) 2.(3, 5) 3.(-2, -5) 4.(-3, -1) Answer Now

9 3) Solve the following equation for y: 2x + y = 4 1.Draw the river 2.Subtract 2x from both sides 3.Simplify. Write the equation with the variable first. -2x -2x y = -2x + 4

10 4) Solve the following equation for y: 4x - 5y = 7 1.Draw the river 2.Subtract 4x from both sides 3.Simplify. Write the equation with the variable first. 4.Divide both sides by -5 5.Does the fraction simplify? -4x -4x -5y = -4x

11 5) Solve the following equation for y: 6x – 2y = 8 1.y = -6x y = 6x – 8 3.y = -3x y = 3x - 4 Answer Now

12 6) Make a table and graph the solution set of 4x + 2y = 6. 1.Draw the river 2.Subtract 4x from both sides 3.Simplify. Write the equation with the variable first. 4.Divide both sides by 2 5.Does the fraction simplify? -4x -4x 2y = -4x

13 Lets use the domain {0, 1, 2} for our equation. Create a t-chart by picking at least three numbers to plug into our equation. x ordered pair y -2(0) (0, 3) -2(1) (1, 1) -2(2) (2, -1)

14 Graph {(0, 3), (1, 1), (2, -1)} Draw a line through your points. It should be a straight line.

15 Graph {(0, 3), (1, 1), (2, -1)}

16 Which is the graph of y = -x + 3? 1.A 2.B 3.C 4.D A B C D Answer Now


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