Application of Lines



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+by=mx+b, where mm is the slope, or constant rate of change, and bb is the yy-intercept. The equation is useful for graphing the line and for interpreting the meaning of the slope and yy-intercept in the context of a real-world application. A more simplified form of the slope-intercept form is y=kxy=kx, where the yy-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=kxy = kx, where kk is a real number known as the constant of proportionality.
  • Direct variation can be used to model real-world situations.