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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.

Video Review

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 .

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