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NAME
DATE
2-2
PERIOD
Study Guide and Intervention
Linear Relations and Functions
Linear Relations and Functions A linear equation has no operations other than
addition, subtraction, and multiplication of a variable by a constant. The variables may not
be multiplied together or appear in a denominator. A linear equation does not contain
variables with exponents other than 1. The graph of a linear equation is always a line.
A linear function is a function with ordered pairs that satisfy a linear equation. Any
linear function can be written in the form f(x) = mx + b, where m and b are real numbers.
If an equation is linear, you need only two points that satisfy the equation in order to graph
the equation. One way is to find the x-intercept and the y-intercept and connect these two
points with a line.
Example 1
x
a linear function? Explain.
Is f(x) = 0.2 - −
5
Yes; it is a linear function because it can be written in the form
1
f(x) = -−
x + 0.2.
5
Is 2x + xy - 3y = 0 a linear function? Explain.
No; it is not a linear function because the variables x and y are multiplied together in the
middle term.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises
State whether each function is a linear function. Write yes or
no. Explain.
18
2. 9x = −
y
1. 6y - x = 7
Yes; it can be written
x
7
+−
.
as y = −
6
6
x
4. 2y- −
-4=0
6
Yes; it can be written
x
+ 2.
as y = −
12
7. f(x) = 4 - x3
No; the variable x is
being multiplied by
itself.
Chapter 2
x
3. f (x) = 2 - −
11
No; the variable y
appears in the
denominator.
11
0.4
6. 0.2x = 100 - −
y
5. 1.6x - 2.4y = 4
Yes; it can be written
5
2
as y = −
x-−
.
3
Yes; it can be written
x
+ 2.
as f(x) = - −
3
4
8. f(x) = −
x
No; the variable y
appears in the
denominator.
9. 2yx - 3y + 2x = 0
No; the variable x
appears in the
denominator.
11
No; the variables x
and y are being
multiplied together.
Glencoe Algebra 2
Lesson 2-2
Example 2
NAME
DATE
2-2
PERIOD
Study Guide and Intervention
(continued)
Linear Relations and Functions
Standard Form
The standard form of a linear equation is Ax + By = C, where
A, B, and C are integers whose greatest common factor is 1.
Example 1
Write each equation in standard form. Identify A, B, and C.
a. y = 8x - 5
y = 8x - 5
-8x + y = -5
8x - y = 5
b. 14x = -7y + 21
14x = -7y + 21
14x + 7y = 21
2x + y = 3
Original equation
Subtract 8x from each side.
Multiply each side by -1.
So A = 8, B = -1, and C = 5.
Original equation
Add 7y to each side.
Divide each side by 7.
So A = 2, B = 1, and C = 3.
Example 2
Find the x-intercept and the y-intercept of the graph of 4x - 5y = 20.
Then graph the equation.
The x-intercept is the value of x when y = 0.
4x - 5y = 20
Original equation
4x - 5(0) = 20
Substitute 0 for y.
x=5
y
2
O
x
6
4
−2
Simplify.
−4
So the x-intercept is 5. Similarly, the y-intercept is -4.
Exercises
Write each equation in standard form. Identify A, B, and C.
2. 5y = 2x + 3
2x - 4y = -1; A = 2,
B = -4, C = -1
3. 3x = -5y + 2
2x - 5y = -3; A = 2,
B = -5, C = -3
3
2
5. −
y=−
x+5
4. 18y = 24x - 9
4
8x - 6y = 3; A = 8,
B = -6, C = 3
7. 0.4x + 3y = 10
6. 6y - 8x + 10 = 0
3
8x - 9y = -60; A = 8,
B = -9, C = -60
8. x = 4y - 7
2x + 15y = 50; A = 2,
B = 15, C = 50
3x + 5y = 2; A = 3,
B = 5, C = 2
4x - 3y = 5; A = 4,
B = -3, C = 5
9. 2y = 3x + 6
x - 4y = -7; A = 1,
B = -4, C = -7
3x - 2y = -6; A = 3,
B = -2, C = -6
Find the x-intercept and the y-intercept of the graph of each equation. Then graph
the equation using the intercepts.
10. 2x + 7y = 14
11. 5y - x = 10
y
12. 2.5x - 5y + 7.5 = 0
y
2
4
2
y
2
O
2
4
6
8x
−2
−4
−2
2
O
4x
−4
−2
−2
O
2
x
−2
x-int: 7; y-int: 2
Chapter 2
x-int: -10; y-int: 2
12
x-int: -3; y-int: 1.5
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. 2x = 4y -1