How to Draw y 5 3x

Draw and understand linear functions

In this section, we'll look at linear functions and how to plot them. First of all, we will clarify once again what a linear function actually is. Then we show how to plot such a function in a coordinate system.

In order to understand the following article well, you need some previous knowledge. If you still have problems solving equations or do not know what a table of values ​​is, you should read it again. However, if you can do this, you can save yourself reading the following articles.

Linear function video:
This article is also available as a video.

  • Notes: This is still a blackboard video. A New edition in HD is planned. It can also be called up directly in the Linear Function Video section.
  • Problems: If you have playback problems, please go to the article Video problems.
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What is a linear function?

Even if many of you are already familiar with this, we would like to take a quick look at what a linear function actually is. The mathematical relationship for school lessons is f (x) = a · x + b. The equation y = a · x + b is often used. A and b are any number, for example 4 or 0.5. You will see that such a function looks like a "straight line" when you draw it. Example of a linear function: f (x) = 2x.

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Draw a linear function

Now that we have clarified what a linear function is, let's draw it. We will now explain in detail how this works using an example. Follow this carefully. However, in order to get really fit with drawing functions, you should complete our exercises and tasks on the topic. Our example shows how to draw f (x) = y = 2x. We start again with a table of values ​​(explanations can be found under this):

And this is how it works with the table of values:

  • First write down the equation y = 2x
  • Draws the horizontal and vertical lines of the table of values
  • Writes x over the left column and y over the right column
  • Write the sequence of numbers from -5 to +5 in the left column
  • Inserts the respective X value into the equation and calculates the Y value in each case
  • Enter the respective Y value in the right column

Next you need to draw an X-Y coordinate system. If you are not yet sure what such a coordinate system looks like, you can read it in our chapter Drawing a coordinate system (link opens in new browser window). The following graphic shows the finished solution. How you come to this is written below.

And this is how drawing linear functions works:

  • Creates the table of values
  • Draws a coordinate system
  • In your table of values, to the right of the x-value, there is also a y-value in a row. You now have to look for the point in the coordinate system where the x-value and y-value are set at the same time. Example: x = -5 and y = - 10. Then you go left on the x-axis until you are on -5. And then you go down from there until you are at the level -10 on the y-axis. At this point you make a small cross. So do you do this for all values.
  • Place the ruler so that you can draw a straight line through all the crosses and draw it. Finished!


Before you start the exercises, you should repeat all the steps for drawing the function f (x) = 2x yourself on paper! Note: The last point (the one with the ruler) only applies to linear functions, since all points here lie on a straight line. This (unfortunately) does not work for other types of functions. We will only get to that in the following chapters.

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