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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)
Answer NowAnswer Now
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 NowAnswer Now
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
Answer NowAnswer Now
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
Answer NowAnswer Now
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