The statement “y varies inversely as x means that when x increases, ydecreases by the same factor. In other words, the expression xy is constant: xy = k.

when one gets bigger, the other gets smaller. When one gets smaller, the other gets bigger. This kind of relationship between two variables is called inverse variation: (Assume all other variables are held constant.)

Direct variation describes a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if: y=kx. for some constant k . This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y.

No, y is not directly proportional to x because there is not a constant of proportionality.

Direct Proportion In mathematical statements, it can be expressed as y = kx. This reads as “y varies directly as x” or “y is directly proportional as x” where k is constant in the equation.

Examples. If an object travels at a constant speed, then the distance traveled is directly proportional to the time spent traveling, with the speed being the constant of proportionality. The circumference of a circle is directly proportional to its diameter, with the constant of proportionality equal to π.

Indirectly Proportional Formula. ab = k; where k is the proportional constant.

Direct proportion is the relationship between two variables whose ratio is equal to a constant value. In other words, direct proportion is a situation where an increase in one quantity causes a corresponding increase in the other quantity, or a decrease in one quantity results in a decrease in the other quantity.

1. Area and side length of a rhombus – This is least proportional as they are inversely proportional. 2. Distance and time when speed is constant is proportional.

Step-by-step explanation: Area and side length of a rhombus – This is least proportional as they are inversely proportional.

Answer. In the graph of a direct proportion, its graph shows a straight line graph or a linear graph that go through the origin. So that makes options A and options D correct. It’s slope is also constant so therefore option C is correct, leaving us option B as the statement that is not true about direct proportion.

Compare the constants of the two variables. changed at the same rate, or by the same factor, then they are directly proportional. For example, since the x-coordinates changed by a factor of 2 while the y-coordinates also changed by a factor of 2, the two variables are directly proportional.

Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the “constant of proportionality”.

Common examples include comparing prices per ounce while grocery shopping, calculating the proper amounts for ingredients in recipes and determining how long car trip might take. Other essential ratios include pi and phi (the golden ratio).

Proportion says that two ratios (or fractions) are equal….Example: Rope

• 40m of that rope weighs 2kg.
• 200m of that rope weighs 10kg.
• etc.

Example of Solving a Complex Proportion

1. First we cross-multiply.
2. Then we distribute the 20 to the x and 1.
3. Subtract 20x from both sides to isolate x.
4. Divide by 10 on both sides.
5. First, distribute to each of the terms inside the parenthesis.
6. Distribute to each of the terms inside the parenthesis.

C1 [ C, + sing/pl verb ] the number or amount of a group or part of something when compared to the whole: Children make up a large proportion of the world’s population. A higher proportion of men are willing to share household responsibilities than used to be the case.

Properties of Proportion

• (i) The numbers a, b, c and d are in proportional if the ratio of the first two quantities is equal to the ratio of the last two quantities, i.e., a : b : : c : d and is read as ‘a is to b is as c is to d’.
• (ii) Each quantity in a proportion is called its term or its proportional.

A ratio is a comparison of two quantities. A proportion is an equality of two ratios.