# Linear and relationship

### Difference Between Proportional & Linear Relationships | Sciencing

More importantly, there exists a numerical measure that assesses the strength of the linear relationship between two quantitative variables with which we can. Definition of linear relationship: A relationship of direct proportionality that, when plotted on a graph, traces a straight line. In linear relationships, any given. A linear equation in two variables describes a relationship in which the value of one of the variables depends on the value of the other variable. In a linear.

Medications, especially for children, are often prescribed in proportion to weight.

This is an example of a linear relationship. Nonlinear relationships, in general, are any relationship which is not linear.

What is important in considering nonlinear relationships is that a wider range of possible dependencies is allowed. When there is very little information to determine what the relationship is, assuming a linear relationship is simplest and thus, by Occam's razor, is a reasonable starting point. However, additional information generally reveals the need to use a nonlinear relationship.

Many of the possible nonlinear relationships are still monotonic. This means that they always increase or decrease but not both. Monotonic changes may be smooth or they may be abrupt. For example, a drug may be ineffective up until a certain threshold and then become effective. However, nonlinear relationships can also be non-monotonic. That is, we typically identify the ordered pairs that describe where the line intersects the x-axis and where it intersects the y-axis.

In the form of ordered pairs, that means we want to know the values a and b in the ordered pairs a,0 and 0,b. The first is the x-axis intercept and the second the y-axis intercept.

When real-life situations are described through linear relationships, the intercepts often take on important meaning.

## Concepts: Linear and Nonlinear

The following example is intended to illustrate that. Here is a table of values to show the cost associated with renting various numbers of Nintendo games.

The cost includes the annual fee plus the per-night rental charge. We can also plot the ordered pairs number of rentals,total costas shown in the graph below.

In symbolic form, we can write an equation to represent the relationship between games rented and total cost. We have shown three different ways to represent the relationship: The fourth representation, verbal, was the original description of the relationship. How does the graph below differ from the one above?

## Linear Relationship

How are they similar? What is the significance of the vertical-axis intercept? Why does only one end of the line segment have arrowheads on it? These and related questions are important to consider when working with representations of relationships.

Here are some questions and answers that help focus on critical aspects of the relationship. Why or why not?

### Concepts: Linear and Nonlinear | NECSI

How is this shown in the graph? Can a club member rent fewer than zero 0 games?

The graph shows this because it stops at the ordered pair 0, In the real world, a member cannot rent a part of a game, because we assume each game is a physical whole that cannot be split into parts.

The graph is deceiving in this way, for the solid line seems to indicate that any value on the horizontal axis is possible. To be more accurate, we could try to draw in many many little dots to indicate only certain values are possible.

However, this is not practical. So we draw in the solid line and then somehow indicate that only whole values are possible.

### Linear relationship - When a changes in two variables correspond

The same is true for the vertical axis. Is there a limit to the number of games that can be rented? We know of no restrictions on the number of games that could be rented.

The segment in the graph shows arrowheads at one end, indicating that the pattern shown to that point continues. In practical terms, there may be some limit to the number of games that can be rented, most likely based on the inventory maintained by Captain Video.