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 .

y = \frac{7}{4} \Leftrightarrow 0 x + 1 y = \frac{7}{4}

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

0

for

x

and solve for

y .

Then, we would substitute

0

for

y

and solve for

x .

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

y -

intercept.

0 x + 1 y = \frac{7}{4}

Substitute

$x = 0$

0 (0) + 1 y = ? \frac{7}{4}

ZeroPropMult

Zero Property of Multiplication

0 + 1 y = ? \frac{7}{4}

IdPropAdd

Identity Property of Addition

1 y = ? \frac{7}{4}

IdPropMult

Identity Property of Multiplication

y = \frac{7}{4}

Everything is going smoothly so far. The

y -

intercept lies on the point

(0, \frac{7}{4}) .

Now let's try the

x -

intercept.

0 x + 1 y = \frac{7}{4}

Substitute

$y = 0$

0 x + 1 (0) = ? \frac{7}{4}

ZeroPropMult

Zero Property of Multiplication

0 + 0 = ? \frac{7}{4}

AddTerms

Add terms

0 \neq = \frac{7}{4}

When we try to find the

x -

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

x -

axis, so it must be horizontal. Note that any time we have an equation in the form

y = b,

where

b

is a real number, the graph of

y = b

will be a horizontal line.

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