Module 5: Background You’ll Need 4

  • Use a linear function to make predictions.

Modeling a Linear Relationship

When Pam first met Kai, he was extremely overweight—almost [latex]100[/latex] pounds overweight, and for this reason alone, his owner wanted him euthanized. Kai’s life was in danger, and he was miserable, but Pam rescued him. Here are the details of Kai’s journey:

  • Initial Weight: Kai weighed [latex]173[/latex] pounds before Pam agreed to foster him. She modified his diet and began walking him three times daily.
  • Constant Rate of Change: A reasonable goal was for Kai to lose about two pounds each week.
The familiar slope-intercept form of a linear equation you probably learned about in algebra is [latex]y=mx+b[/latex], where

  • [latex]x[/latex] represents the explanatory (independent) variable represented on the horizontal axis.
  • [latex]y[/latex] represents the response (dependent) variable represented on the vertical axis.
  • [latex]m[/latex] represents the constant rate of change (the slope), and
  • [latex]b[/latex] represents the initial value in a given scenario (which can be zero or negative).