Math Lesson 14.1.3 - Vertical Linear Graphs

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Welcome to our Math lesson on Vertical Linear Graphs, this is the third lesson of our suite of math lessons covering the topic of Linear Graphs, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Vertical Linear Graphs

If a linear graph is vertical, this means that the x-coordinate does not change. This means that all points of the graph have the same x-coordinate for every value of y. In this way, we don't need a y-coordinate in vertical graphs; the only important information in such graphs is their x-coordinate, which shows how much on the left or on the right of the vertical axis the graph of the line lies. The figure below shows three vertical graphs: x = 3, x = 0 and x = -4.

It is obvious that this time, the only variable present in the equation is the independent variable x. it is true that the equation of a line in two dimensions is

but since the y-variable is not important, we omit it by multiplying the variable y by zero. This means b = 0. Therefore, the line equation becomes

or

The x-intercept of the graph is at

For example, the line x = 3 may be the simplified form of 2x - 6 = 0, -5x + 15 = 0, etc. This is because

and so on.

Example 2

1. Calculate the distance between the lines 2x - 7 = 0 and 3x + 2 = 0.
2. Make a figure that shows both of these lines.

Solution 2

1. First, we must find the values of x for each line. Thus, for the first line we have
   2x - 7 = 0
   2x = 7
   x = 7/2
   and for the second line, we have
   3x + 2 = 0
   3x = -2
   x = -2/3
   Since they are on the opposite sides of the vertical axis, we must add these two numbers (without considering the sign) to find the distance between the given lines. Hence, the required distance D is
   D = 7/2 + 2/3
   = 21/6 + 4/6
   = 26/6 units
2. The figure that includes both lines is shown below.

More Linear Graphs Lessons and Learning Resources

Whats next?

Enjoy the "Vertical Linear Graphs" math lesson? People who liked the "Linear Graphs lesson found the following resources useful:

1. Vertical Feedback. Helps other - Leave a rating for this vertical (see below)
2. Linear Graphs Math tutorial: Linear Graphs. Read the Linear Graphs math tutorial and build your math knowledge of Linear Graphs
3. Linear Graphs Revision Notes: Linear Graphs. Print the notes so you can revise the key points covered in the math tutorial for Linear Graphs
4. Linear Graphs Practice Questions: Linear Graphs. Test and improve your knowledge of Linear Graphs with example questins and answers
5. Check your calculations for Linear Graphs questions with our excellent Linear Graphs calculators which contain full equations and calculations clearly displayed line by line. See the Linear Graphs Calculators by iCalculator™ below.
6. Continuing learning linear graphs - read our next math tutorial: Slopes and Gradients

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