# Direct and inverse relationship function

### What Is the Difference Between a Direct and an Inverse Relationship? | Sciencing

The relationship between two variables is a direct relationship if when one increases so does the other or as one decreases so does the other. The radius of a. Direct & Inverse Relationships. Direct Relationships In a direct relationship, as “x” increases “y” increases proportionally. On the graph you see a straight. This page contains a short article on direct and inverse relationships.

If you increase the independent variable x, such as the diameter of the circle or the height of the ball dropthe dependent variable increases too and vice-versa.

Sciencing Video Vault A direct relationship is linear. Pi is always the same, so if you double the value of D, the value of C doubles too.

## Intro to direct & inverse variation

The gradient of the graph tells you the value of the constant. Inverse Relationships Inverse relationships work differently.

**Direct Inverse and Joint Variation Word Problems**

If you increase x, the value of y decreases. For example, if you move more quickly to your destination, your journey time will decrease. In this example, x is your speed and y is the journey time.

Doubling your speed halves the journey time, and increasing the speed by ten times makes the journey time ten times shorter.

Mathematically, this type of relationship has the form: As you start to increase x, y decreases really quickly, but as you continue increasing x the rate of decrease of y gets slower. In this case, y is inversely related to x. At first an increase of 3 in x decreases y by 2, but then an increase of 6 in x only decreases y by 1. This is why inverse relationships are declining curves that get shallower the further you move along them. The Difference In direct relationships, an increase in x leads to a correspondingly sized increase in y, and a decrease has the opposite effect.

This makes a straight-line graph.

As one increases, the other decreases and vice versa. Direct Variation Consider the case of someone who is paid an hourly wage. The amount of pay varies with the number of hours worked.

This is an important component of direct variation: When one variable is 0, the other must be 0 as well.

## Variation, Direct and Inverse

So, if two variables vary directly and one variable is multiplied by a constant, then the other variable is also multiplied by the same constant. If one variable doubles, the other doubles; if one triples, the other triples; if one is cut in half, so is the other. In the preceding example, the equation is y 12x, with x representing the number of hours worked, y representing the pay, and 12 representing the hourly rate, the constant of proportionality. Graphically, the relationship between two variables that vary directly is represented by a ray that begins at the point 0, 0 and extends into the first quadrant.

### Direct and inverse relationships - Math Central

In other words, the relationship is linear, considering only positive values. See part a of the figure on the next page. The slope of the ray depends on the value of k, the constant of proportionality.

The bigger k is, the steeper the graph, and vice versa. Inverse Variation When two variables vary inversely, one increases as the other decreases. As one variable is multiplied by a given factor, the other variable is divided by that factor, which is, of course, equivalent to being multiplied by the reciprocal the multiplicative inverse of the factor.

For example, if one variable doubles, the other is divided by two multiplied by one-half ; if one triples, the other is divided by three multiplied by one-third ; if one is multiplied by two-thirds, the other is divided by two-thirds multiplied by three-halves.

Consider a situation in which miles are traveled. If traveling at an average rate of 5 miles per hour mphthe trip takes 20 hours.

If the average rate is doubled to 10 mph, then the trip time is halved to 10 hours. If the rate is doubled again, to 20 mph, the trip time is again halved, this time to 5 hours.