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# Horizontal and Vertical Line Graphs

## Line y = # is parallel to x-axis and line x = # is parallel to y-axis

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Practice Horizontal and Vertical Line Graphs
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Horizontal and Vertical Line Graphs

Suppose you're at an all-you-can-eat pancake house where you can pay $8.99 and have all the pancakes you want. What if you graphed the number of pancakes you ate along the $x-$ axis and the amount of money you have to pay along the $y-$ axis. Would the line representing this situation be horizontal or vertical? In this Concept, you'll learn about horizontal and vertical lines so that you'll be able to create a graph for this type of scenario. ### Guidance Not all graphs are slanted or oblique . Some are horizontal or vertical. Read through the next situation to see why. #### Example A “Mad-cabs” have an unusual offer going on. They are charging$7.50 for a taxi ride of any length within the city limits. Graph the function that relates the cost of hiring the taxi $(y)$ to the length of the journey in miles $(x)$ .

Solution: No matter the mileage, your cab fare will be \$7.50. To see this visually, create a graph. You can also create a table to visualize the situation.

# of miles $(x)$ Cost $(y)$
0 7.50
10 7.50
15 7.50
25 7.50
60 7.50

Because the mileage can be anything, the equation should relate only to the restricted value, in this case, $y$ . The equation that represents this situation is:

$y=7.50$

Whenever there is an equation of the form $y= \text{constant}$ , the graph is a horizontal line that intercepts the $y-$ axis at the value of the constant.

Similarly, if there is an equation of the form $x=\text{constant}$ , the graph is a vertical line that intercepts the $x-$ axis at the value of the constant. Notice that this is a relation but not a function because each $x$ value (there’s only one in this case) corresponds to many (actually an infinite number of) $y$ values.

#### Example B

Graph $y=-2$ by making a table and plotting the points.

Solution:

Notice that there is no $x$ in this equation. So, no matter what the value of $x$ is, $y$ will always be -2. A table of points on this line will look like the following:

$(x)$ $(y)$
$-2$ $-2$
$-1$ $-2$
$0$ $-2$
$1$ $-2$
$2$ $-2$

#### Example C

Graph the following lines.

(a) $y=4$

(b) $y=-4$

(c) $x=4$

(d) $x=-4$

Solution:

(a) $y=4$ is a horizontal line that crosses the $y-$ axis at 4.

(b) $y=-4$ is a horizontal line that crosses the $y-$ axis at –4.

(c) $x=4$ is a vertical line that crosses the $x-$ axis at 4.

(d) $x=-4$ is a vertical line that crosses the $x-$ axis at –4.

### Guided Practice

Graph the following:

1. $y=-3$

2. $x=5$

Solutions:

The graph of $y=-3$ is a horizontal line where $y$ is always equal to 3 no matter what $x$ is, and the graph of $x=5$ is a vertical line where $x$ is always equal to 5 no matter what $y$ is:

### Practice

1. What is the equation for the $x-$ axis ?
2. What is the equation for the $y-$ axis ?

Write the equations for the graphed lines pictured below.

1. $E$
2. $B$
3. $C$
4. $A$
5. $D$
1. Graph $x=-7$ .
2. Graph $y=100$ .
3. Graph $y=1/2$ .

### Vocabulary Language: English Spanish

oblique graph

oblique graph

A graph is oblique if it is slanted, rather than horizontal or vertical.
Horizontally

Horizontally

Horizontally means written across in rows.
Vertically

Vertically

Vertically means written up and down in columns.