Exercise 9 Page 159

We want to graph the given equation using a table of values. First we will select some arbitrary values from the domain. Then we will substitute them for

x

in the equation. Because we were not given any restrictions to the possible values of

x,

the domain of this equation is all real numbers.

Domain : All real numbers

This means that we can choose any values of

x

that we want. We will use

0,

2,

and

4 .

Solving for

y

will give us the corresponding values from the range.

$x$	$x + 2 y = 4$	Simplify
$0$	$0 + 2 y = 4$	$y = 2$
$2$	$2 + 2 y = 4$	$y = 1$
$4$	$4 + 2 y = 4$	$y = 0$

Using these $x$ and $y$ values as $(x, y) -$ coordinate pairs, we can plot the points. Connecting these points will give us the graph of the equation.

Extra

Solving for

y

In the table, we solved for

y

in three different equations. We did this using the Properties of Equality. Let's see how this was done for each of the equations! We only needed to use one property to solve the first equation — the Division Property of Equality.

0 + 2 y = 4

AddTerms

Add terms

2 y = 4

DivEqn

$LHS / 2 = RHS / 2$

\frac{2 y}{2} = \frac{4}{2}

CalcQuot

Calculate quotient

y = 2

We needed to use two properties n the second and third equations, the Subtraction Property of Equality and the Division Property of Equality.

	Second Equation	Third Equation
Equation	$2 + 2 y = 4$	$4 + 2 y = 4$
Subtraction Property of Equality	$2 + 2 y - 2 = 4 - 2$	$4 + 2 y - 4 = 4 - 4$
Subtract Terms	$2 y = 2$	$2 y = 0$
Division Property of Equality	$\frac{2 y}{2} = \frac{2}{2}$	$\frac{2 y}{2} = \frac{0}{2}$
Divide	$y = 1$	$y = 0$