Download Tables and Relations

5-3 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
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=4
What 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)
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••
•
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Connect the points on your graph.
What does the graph look like?
It is a straight line! It is a linear relation.
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What does the line
represent?
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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!
1) Which is a solution to
2x – y = 5?
1.
2.
3.
4.
(2, 1)
(3, 2)
(4, 3)
(5, 4)
Answer Now
2) Which ordered pair is
not a solution to the graph
shown?
1.
2.
3.
4.
(0, -1)
(3, 5)
(-2, -5)
(-3, -1)
Answer 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 = 7
1. Draw “the river”
-4x
-4x
2. Subtract 4x from
both sides
-5y = -4x + 7
3. Simplify. Write
-5
-5
the equation with
the variable first.
4. Divide both sides
by -5
5. Does the fraction
simplify?
4 x  7
y
5
5) Solve the following equation for y:
6x – 2y = 8
1.
2.
3.
4.
y = -6x + 8
y = 6x – 8
y = -3x + 4
y = 3x - 4
Answer Now
6) Make a table and graph the solution set of
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 + 2y = 6.
-4x
-4x
2y = -4x + 6
2
2
y  2 x  3
Create a t-chart by picking at least three
numbers to plug into our equation.
y  2 x  3
Let’s use the domain {0, 1, 2} for our equation.
x
y  2 x  3
y
0
1
2
-2(0) + 3
-2(1) + 3
-2(2) + 3
3
1
-1
ordered pair
(0, 3)
(1, 1)
(2, -1)
Graph {(0, 3), (1, 1), (2, -1)}
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•
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Draw a line through your points. It should
be a straight line.
Graph {(0, 3), (1, 1), (2, -1)}
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Which is the graph of y = -x + 3?
B
A
D
C
1.
2.
3.
4.
A
B
C
D
Answer Now