Example4.5.7

Let's review. With a simple equation like \(y=2x+3\text{,}\) we can see that there 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 you would increase the \(x\)-value by \(1\text{,}\) the \(y\)-value increases by \(2\text{.}\) With these basic observations, you may 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 \(2\)
in-context