Drawing Straight-Line Graphs

Once you have a table of values, each column $(x, y)$ is a point. Plot the points on the Cartesian plane and, for a rule like $y = 2x + 1$, they line up perfectly straight — so you join them with a ruler and extend the line. Rules of the form $y = mx + c$ always give straight lines, which is why they are called linear.

One point is especially easy: where the line crosses the $y$-axis. That happens when $x = 0$, so for $y = 2x + 1$ we get $y = 2(0) + 1 = 1$ — the line cuts the $y$-axis at $y = 1$.

Worked example. Does $(2, 7)$ lie on $y = 3x + 1$?

Test it: $3(2) + 1 = 7$. The $y$-value matches, so yes, the point is on the line.