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We are going to learn how to graph linear functions quickly without using tables of values or extensive procedures.
Let’s start by analyzing the general form of a linear function
The slope of a linear function is only a variation of the inclination of the straight line that joins two points, and that is given by the following equation:
In a nutshell, the slope is:
These «variations» are basically moving forward or backward from a starting point.
The starting point to make the graph in the way we propose here is the intercept with the Y axis.
Let’s look at an example:
In this case our starting point is the intercept with the Y axis, that is 1. And from there we simply analyze the variations indicated by the slope and then proceed to join both points, resulting in the straight line of the function:
Let’s analyze another example: In the following image we see that our starting point is 2, and the slope tells us that the other important point to join the line is 3 units down (because it is negative) and 4 units to the right (the denominator is considered positive).
Do you need more examples? I invite you to take a look at this video class. There you will find more examples solved step by step and you will realize how simple it is.
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