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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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**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.

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**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

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**x + y = 4 What about decimals? If x = 2.6 then y = ?**

Now, let’s graph the pairs of numbers we have listed.

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

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**It is a straight line! It is a linear relation.**

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

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**1) Which is a solution to 2x – y = 5?**

(2, 1) (3, 2) (4, 3) (5, 4) Answer Now

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**2) Which ordered pair is not a solution to the graph shown?**

(0, -1) (3, 5) (-2, -5) (-3, -1) Answer Now

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**3) Solve the following equation for y: 2x + y = 4**

Draw “the river” Subtract 2x from both sides Simplify. Write the equation with the variable first. -2x x y = -2x + 4

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**4) Solve the following equation for y: 4x - 5y = 7**

Draw “the river” Subtract 4x from both sides Simplify. Write the equation with the variable first. Divide both sides by -5 Does the fraction simplify? -4x x -5y = -4x + 7

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**5) Solve the following equation for y: 6x – 2y = 8**

Answer Now

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**6) Make a table and graph the solution set of 4x + 2y = 6.**

Draw “the river” Subtract 4x from both sides Simplify. Write the equation with the variable first. Divide both sides by 2 Does the fraction simplify? -4x x 2y = -4x + 6

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**Let’s use the domain {0, 1, 2} for our equation.**

Create a t-chart by picking at least three numbers to plug into our equation. Let’s use the domain {0, 1, 2} for our equation. x 1 2 ordered pair y -2(0) (0, 3) -2(1) (1, 1) -2(2) (2, -1)

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**Draw a line through your points. It should be a straight line.**

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

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Graph {(0, 3), (1, 1), (2, -1)} • • •

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**Which is the graph of y = -x + 3?**

B A D C A B C D Answer Now

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Solving Equations with Variable on Both Sides Objective: Students will solve equations with variables on both sides. Section 3.4.

Solving Equations with Variable on Both Sides Objective: Students will solve equations with variables on both sides. Section 3.4.

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