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 \(2\)
in-context