###### Example4.2.7

Let's plot a graph for the equation \(y=-2x+5\text{.}\) We use a table to organize our work:

\(x\) | \(y=-2x+5\) | Point |

\(-2\) | \(\phantom{-2(-2)+5=\substitute{9}}\) | \(\phantom{(-2,9)}\) |

\(-1\) | \(\phantom{-2(-1)+5=\substitute{7}}\) | \(\phantom{(-1,7)}\) |

\(0\) | \(\phantom{-2(0)+5=\substitute{5}}\) | \(\phantom{(0,5)}\) |

\(1\) | \(\phantom{-2(1)+5=\substitute{3}}\) | \(\phantom{(1,3)}\) |

\(2\) | \(\phantom{-2(2)+5=\substitute{1}}\) | \(\phantom{(2,1)}\) |

\(x\) | \(y=-2x+5\) | Point |

\(-2\) | \(-2(-2)+5=\substitute{9}\) | \((-2,9)\) |

\(-1\) | \(-2(-1)+5=\substitute{7}\) | \((-1,7)\) |

\(0\) | \(-2(0)+5=\substitute{5}\) | \((0,5)\) |

\(1\) | \(-2(1)+5=\substitute{3}\) | \((1,3)\) |

\(2\) | \(-2(2)+5=\substitute{1}\) | \((2,1)\) |

We use points from the table to graph the equation. First, plot each point carefully. Then, connect the points with a smooth curve. Here, the curve is a straight line. Lastly, we can communicate that the graph extends further by sketching arrows on both ends of the line.