Mathematicians, physicists and engineers have many terms to describe mathematical relationships. There is usually some logic to the names chosen, although this is not always apparent if you are not aware of the math behind it. Once you understand the concept involved the connection to the chosen words becomes obvious. Show TL;DR (Too Long; Didn't Read)The relationship between variables can be linear, non-linear, proportional or non-proportional. A proportional relationship is a special kind of linear relationship, but while all proportional relationships are linear relationships, not all linear relationships are proportional. Proportional RelationshipsIf the relationship between “x” and “y” is proportional, it means that as “x” changes, “y” changes by the same percentage. Therefore, if “x” grows by 10 percent of “x,” “y” grows by 10 percent of “y.” To put it algebraically: y = mx where “m” is a constant. Consider a non-proportional relationship. Children look different than adults, even in photographs where there is no way to tell exactly how tall they are, because their proportions are different. Children have shorter limbs and bigger heads compared to their bodies than adults do. Children's features, therefore, grow at disproportionate rates as they become adults. Linear RelationshipMathematicians love to graph functions. A linear function is very easy to graph, because it is a straight line. Expressed algebraically, linear functions take the form y = mx + b where “m” is the slope of the line and “b” is the point where the line crosses the “y” axis. It is important to note that “m” or “b” or both constants can be zero or negative. If “m” is zero, the function is simply a horizontal line at a distance of “b” from the “x” axis. The DifferenceProportional and linear functions are almost identical in form. The only difference is the addition of the “b” constant to the linear function. Indeed, a proportional relationship is just a linear relationship where b = 0, or to put it another way, where the line passes through the origin (0, 0). So a proportional relationship is just a special kind of linear relationship, i.e., all proportional relationships are linear relationships (although not all linear relationships are proportional). Examples of Proportional and Linear RelationshipsA simple illustration of a proportional relationship is the amount of money you earn at a fixed hourly wage of $10 an hour. At zero hours, you have earned zero dollars, at two hours, you have earned $20 and at five hours you have earned $50. The relationship is linear because you get a straight line if you graph it, and proportional because zero hours equals zero dollars. Compare this with a linear but non-proportional relationship. For example, the amount of money you earn at $10 an hour in addition to a $100 signing bonus. Before you start working (that is, at zero hours) you have $100. After one hour, you have $110, at two hours $120, and at five hours $150. The relationship still graphs as a straight line (making it linear) but is not proportional because doubling the time you work does not double your money. Related ArticlesWhat Is a Non Linear Relationship?How to Find the Period of a FunctionWhat Is the Difference Between a Direct and an Inverse...How to Calculate Time With 100 Minute ClockHow to Become Good at MathHow to Tell If Lines Are Parallel, Perpendicular or...How Many Earth Days Equals One Year on Venus?How to Figure out Scale Intervals on a GraphHow to Create Pictures With Math FunctionsHow to Find the Slope of a Nonlinear LineHow to Calculate Cost Increase by a PercentHow to Find a Parallel LineWhat Are the Similarities and Differences Between a...How to Find the X Intercept of a FunctionNesting Habits of Wild RabbitsHow to Calculate an Average Percent ChangeHow is Calculus Used in Economics?The Similarities & Differences Between Rational Expressions...How Are Conifers & Ferns Different?How to Plot Line Segments on Graphing CalculatorReferences
About the Author Tom Kantain has been writing and editing in various forms for over 20 years. He has written a regular magazine column on the philosophy of games. Kantain holds a Master of Arts in philosophy as well as a Bachelor of Laws. Ist eine proportionale Funktion linear?Fazit: Jede proportionale Funktion ist auch eine lineare Funktion - jedoch nicht umgekehrt. Der Unterschied zwischen beiden Funktionstypen ist im y-Achsenabschnitt b "versteckt".
Warum ist nicht jede lineare Funktion eine proportionale Funktion?Lineare Funktionen kennenlernen
Der Graph einer proportionalen Funktion y=f(x)=mxist eine Gerade durch den Ursprung. Umgekehrt ist jede Gerade durch den Koordinatenursprung, die nicht gleich der y-Achse ist, der Graph einer proportionalen Funktion.
Wann ist etwas linear?Der Graph einer linearen Funktion ist immer eine Gerade, dies liegt daran, dass das Verhältnis der zwei Variablen antiproportional ist. Der Graph einer linearen Funktion ist immer eine Gerade, dies liegt daran, dass das Verhältnis der zwei Variablen proportional ist.
Wie erkenne ich ob es proportional ist?Eine Zuordnung ist dann proportional, wenn mit einem gleichbleibenden (positiven) Faktor multipliziert wird. Den Faktor nennt man dann Proportionalitätsfaktor. Für eine proportionale Zuordnung gilt die Aussage „je mehr, desto mehr“. Wenn diese verletzt ist, ist die Zuordnung nicht proportional.
|
Ist proportional das gleiche wie linear?
zusammenhängende Posts
Urheberrechte © © 2024 WIKIFI Inc.
