4-4 Equations as Relations

Objectives1. use an equation to determine the range for a given domain

2. graph the solution set for a given domain

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.

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

x + y = 4What about decimals?

If x = 2.6 then y = ?

y = 1.4

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

(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.

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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•What does the line

represent?

1) Which is a solution to2x – y = 5?

1. (2, 1)

2. (3, 2)

3. (4, 3)

4. (5, 4)

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

shown?

1. (0, -1)

2. (3, 5)

3. (-2, -5)

4. (-3, -1)

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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

4) Solve the following equation for y: 4x - 5y = 71. 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 + 7

-5 -5

4 7

5

xy

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

1. y = -6x + 8

2. y = 6x – 8

3. y = -3x + 4

4. y = 3x - 4

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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 + 6

2 2

2 3y x

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

2 3y x

Create a t-chart by picking at least three numbers to plug into our equation.

x

0 1 2

ordered pairy2 3y x

-2(0) + 3 3 (0, 3)

-2(1) + 3 1 (1, 1)

-2(2) + 3 -1 (2, -1)

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?

1. A2. B3. C4. D

A B

C D

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