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 \(2\)
A cartesian graph with the points plotted from the table;there is a line passing through the points and slope triangles drawn between each pair of points
in-context