# Application of Lines

## Overview

### Description

Applications of lines include the use of equations or graphs of lines to model real-world situations and natural phenomena in order to make predictions and solve problems. Situations with a constant rate of change can be described by linear equations. A linear equation can be written in slope-intercept form as $y=mx+b$, where $m$ is the slope, or constant rate of change, and $b$ is the $y$-intercept. The equation is useful for graphing the line and for interpreting the meaning of the slope and $y$-intercept in the context of a real-world application. A more simplified form of the slope-intercept form is $y=kx$, where the $y$-intercept is zero. This is the general form of a direct variation relationship, which models situations that vary proportionally.

### At A Glance

• The slope of a line represents the rate of change of the dependent variable with respect to the independent variable.
• Slope can be interpreted in many real-world relationships, such as speed, unit cost, and rates of change.
• Two variables vary directly if they are related by an equation of the form $y = kx$, where $k$ is a real number known as the constant of proportionality.
• Direct variation can be used to model real-world situations.