Difference between linear and proportional function

What you need:

• Concept of function

Proportional function - what is it?

• Most are familiar with proportional sizes because they are used in the rule of three. Two quantities are proportional to one another if they are in the same Dimensions change: If you double (or halve) one size, you double (or halved) the other size is also reduced. The best examples of this are the quantity of goods and the price that you have to pay.
• Of course, you can also interpret this proportional relationship as a function. This has the general form y = m _* x. Here x and y are the two quantities and m the proportionality factor, for example the price per kilogram (or liter).
• If you plot this function in a coordinate system, you get a straight line with the slope m, which goes through the origin.

Linear function - there is a difference here

• In contrast, a linear function has the general form y = m _* x + b. The formation of the term stems from the fact that the variable "x" occurs linearly, i.e. in the first power.
• Even linear ones Functions have a straight line as an image, but this generally does not go through the origin, but intersects the y-axis at "b".


Linear and exponential - difference

Especially in school lessons you have probably heard the terms "linear" and ...

• Linear functions also correspond to non-proportional quantities (this is due to section "b"). A good example here can be energy costs, where you first pay a base amount "b", plus consumption, the costs of which then develop proportionally.
• However: all proportional functions are contained in the larger set of linear functions. Namely, they correspond to the case b = 0.

Conclusion: Every proportional function is also a linear function - but not the other way around. The difference between the two types of functions is "hidden" in the y-axis intercept b.