AF1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.

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AF1.0 Students write verbal expressions and
sentences as algebraic expressions and equations
they evaluate algebraic expressions, solve simple
linear equations, and graph and interpret their
results. Also covered NS2.3
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Vocabulary
linear equation
An equation whose solutions form a straight line
on a coordinate plane.
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Example 1 Finding Solutions of Equations with
Two Variables Use the given x-values to write
solutions of the equation as ordered pairs.
y 4x 2 x 1, 2, 3,
4.
(x, y)
x 4x 2 y
1 4(1) 2 6
2 4(2) 2 10
3 4(3) 2 14
4 4(4) 2 18
(1, 6)
(2, 10)
(3, 14)
(4, 18)
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Check if an ordered pair is a solution of an
equation by putting the x and y values into the
equation to see if they make it a true statement.
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Example 2 Checking Solutions of Equations with
Two Variables Determine whether the ordered pair
is a solution to the given equation.
(3, 21) y 7x
y 7x
?
So (3, 21) is a solution to y 7x.
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Additional Example 2B Checking Solutions of
Equations with Two Variables Determine whether
the ordered pair is a solution to the given
equation.
(3, 4) y x 7
y x 7
?
So (3, 4) is not a solution to y x 7.
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Check It Out! Example 2B Determine whether the
ordered pair is a solution to the given equation.
(3, 2) y x 5
y x 5
?
So (3, 2) is not a solution to y x 5.
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You can also graph the solutions of an equation
on a coordinate plane. When you graph the ordered
pairs given by some equations, they form a
straight line. For this reason, these equations
are called linear equations.
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Example 3 Reading Solutions on Graphs Use the
graph of the linear equation to find the value of
y for the given value of x. x 4
When x 4, y 2.
The ordered pair is (4, 2).
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Example 4 Graphing Linear Functions Graph the
equation y x 2.
x x 2 y
1 (1) 2 1
0 (0) 2 2
1 (1) 2 3
(x, y)
(1, 1)
(0, 2)
(1, 3)
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Example 4 Continued
5
4
3
2
1
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
-2
-3
-4
-5
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Check It Out! Example 1 Use the given x-values
to write solutions of the equation as ordered
pairs. y 3x
2 x 2, 3, 4, 5.
x 3x 2 y
2 3(2) 2 8
3 3(3) 2 11
4 3(4) 2 14
5 3(5) 2 17
(x, y)
(2, 8)
(3, 11)
(4, 14)
(5, 17)
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Check It Out! Example 2 Determine whether the
ordered pair is a solution to the given equation.
(4, 20) y 5x
y 5x
?
So, yes (4, 20) is a solution to y 5x.
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Check It Out! Example 3 Use the graph of the
linear function to find the value of y for the
given value of x. x 2
When x 2, y 4.
The ordered pair is (2, 4).
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Check It Out! Example 4 Graph the equation. y
x 4
x x 4 y
1 (1) 4 3
0 (0) 4 4
1 (1) 4 5
(x, y)
(1, 3)
(0, 4)
(1, 5)
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Check It Out! Example 4 Continued
5
4
3
2
1
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
-2
-3
-4
-5