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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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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 xaxis and the amount of money you have to pay along the yaxis. 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=constant, the graph is a horizontal line that intercepts the yaxis at the value of the constant.

Similarly, if there is an equation of the form x=constant, the graph is a vertical line that intercepts the xaxis 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
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 yaxis at 4.

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

(c) x=4 is a vertical line that crosses the xaxis at 4.

(d) x=4 is a vertical line that crosses the xaxis 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 xaxis?
  2. What is the equation for the yaxis?

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.

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