Example4.9.2Building a Table of \(x\)- and \(y\)-values

First, we will graph \(y=-2x+1\) by building a table of values. In theory this method can be used for any type of equation, linear or not. Every student must feel comfortable with building a table of values based on an equation.

\(x\)-value \(y\)-value Point
\(\highlight{-2}\) \(y=-2(\substitute{-2})+1=5\) \((-2,5)\)
\(\highlight{-1}\) \(y=-2(\substitute{-1})+1=3\) \((-1,3)\)
\(\highlight{0}\) \(y=-2(\substitute{0})+1=1\) \((0,1)\)
\(\highlight{1}\) \(y=-2(\substitute{1})+1=-1\) \((1,-1)\)
\(\highlight{2}\) \(y=-2(\substitute{2})+1=-3\) \((2,-3)\)
This is a graph of the line y=-2x+1. The following points on the line are plotted: (-2,5),(-1,3),(0,1),(1,-1),(2,-3).
Table4.9.3Table for \(y=-2x+1\)
Figure4.9.4Graphing \(y=-2x+1\) by Building a Table of Values