###### Example 4.5.7

With a simple equation like \(y=2x+3\text{,}\) we can see that this is a line whose slope is \(2\) and which has initial value \(3\text{.}\) So starting at \(y=3\) when \(x=0\) (that is, on the \(y\)-axis), each time we increase the \(x\)-value by \(1\text{,}\) the \(y\)-value increases by \(2\text{.}\) With these basic observations, we can quickly produce a table and/or a graph.

\(x\) | \(y\) | ||

start on \(y\)-axis \(\longrightarrow\) |
\(0\) | \(3\) | initial \(\longleftarrow\) value |

increase by \(1\longrightarrow\) |
\(1\) | \(5\) | increase \(\longleftarrow\) by \(2\) |

increase by \(1\longrightarrow\) |
\(2\) | \(7\) | increase \(\longleftarrow\) by \(2\) |

increase by \(1\longrightarrow\) |
\(3\) | \(9\) | increase \(\longleftarrow\) by \(2\) |

increase by \(1\longrightarrow\) |
\(4\) | \(11\) | increase \(\longleftarrow\) by \(2\) |