*
Algebra I Lesson 10
Number Relations (Grades 9-12)*

**Instruction 10-3**

**Ordered
Pairs |Relations | Equations as
Relations | Graphing Linear Relations
| Summary**

**EQUATIONS AS RELATIONS**

CACS Algebra 16.0

Any equation represents a set of ordered pairs or a relation. For
example, the equation *y* = 3*x* – 4 where x is an integer and –3
<* x* < 5 represents the relation S = {(–2, –10), (–1, –7), (0, –4),
(1, –1), (2, 2), (3, 5), (4, 8)}. That is, each pair of S satisfies the
given equation.

Having one of the elements of an ordered pair of an equation, we can find
the second element. For example, let x = 3 be first element of an order pair
that fits in the equation y = –x + 7. Replacing x = 3 in the equation gives
us

y= –(3) + 7.

= 4.

So, (3, 4) is an ordered pair of the equation y = –*x* + 7.

The set of all the ordered pairs that fit in an equation is called the set
of the solution. In linear equations, the set of the solutions usually have
infinite numbers of ordered pairs. For example, the set of the solution of
the equation y = –3*x* + 12 is a set of infinite ordered pairs.

**Practice 7**

In equation y = –4*x* – 4, *x* is an integer and –4 < *x *<1.
Find the set of the solution of the equation.

**Solution**

Replace x = –3, –2, –1, 0 in the equation to find the corresponding *y*’s.

x= –3y= –4(–3) – 4

= 12 – 4

= 8

x= –2y= –4(–2) – 4

= 8 – 4

= 4

x= –1y= –4(–1) – 4

= 4 – 4

= 0

x= 0y= –4(0) – 4

= 0 – 4

= –4.

Thus, the set of the solutions of the equation is {(–3, 8), (–2, 4), (–1, 0), (0, –4)}.

**
Real Life Application 1**

Equation *F* = *C* + 32 represents the relation between Celsius degrees
and Fahrenheit degrees. Let (*c*, *f*) represents an ordered pair of
this relation, where *c* is in Celsius degrees and *f* is in
Fahrenheit degrees. Which of the following pairs belong to this relation?

(–5, 23), (–6, 25), (10, 50), (12, 42), (35, 95)

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