To determine if the graph of the given equation is a horizontal or vertical line, let's first consider how the given equation would be written in standard form,

A x + B y = C .

x = - 1.8 \Leftrightarrow 1 x + 0 y = - 1.8

Normally, when graphing a line using the standard form, we would substitute

0

for

y

and solve for

x .

Then, we would substitute

0

for

x

and solve for

y .

Let's try this method using our standard form equation. We will start with the

x -

intercept.

1 x + 0 y = - 1.8

Substitute

$y = 0$

1 x + 0 (0) = ? - 1.8

ZeroPropMult

Zero Property of Multiplication

1 x + 0 = ? - 1.8

IdPropAdd

Identity Property of Addition

1 x = ? - 1.8

IdPropMult

Identity Property of Multiplication

x = - 1.8

Everything is going smoothly so far. The

x -

intercept lies on the point

(- 1.8, 0) .

Now let's try the

y -

intercept.

1 x + 0 y = - 1.8

Substitute

$x = 0$

1 (0) + 0 y = ? - 1.8

ZeroPropMult

Zero Property of Multiplication

0 + 0 = ? - 1.8

AddTerms

Add terms

0 \neq = - 1.8

When we try to find the

y -

intercept of the given equation, we create a contradiction. This means that the line does not cross the

y -

axis, and must be vertical. Note that any time we have an equation in the form

x = a,

where

a

is a real number, the graph of

x = a

will be a vertical line.

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