Graphing Linear Equations from a Table

The three steps

Step 1: pick easy $x$-values. Small numbers around zero, like $-1$, $0$, $1$, and $2$, keep the arithmetic light and the points on your grid.

Step 2: substitute each $x$ into the equation to get its $y$. Follow the order of operations — multiply before you add or subtract. Each row of the table becomes an ordered pair $(x, y)$.

Step 3: plot the pairs and draw a straight line through them, extending past the points in both directions. The graph below shows $y = 2x - 1$ with the four points from the table $(-1, -3)$, $(0, -1)$, $(1, 1)$, and $(2, 3)$.

Choosing good x-values

Always include $x = 0$ — it takes one step to compute and hands you the $y$-intercept, the point where the line crosses the $y$-axis. Then add a negative value or two so your line is anchored on both sides of the axis.

There is no wrong choice, only slow ones. If the equation has a fraction in it, like $y = \dfrac{1}{2}x + 3$, pick even $x$-values so the $y$-values come out whole and easy to plot.

The built-in check

Points from a linear equation must line up perfectly straight. Equal steps in $x$ produce equal steps in $y$ — if $y$ drops by $3$ from one row to the next, it drops by $3$ every time.

The table below is the one behind the graph up top, $y = 2x - 1$. Each step right of $1$ in $x$ raises $y$ by exactly $2$ — that steady jump is the signature of a straight line.

So if three of your points form a line and the fourth sits off to the side, the fourth row of your table has an arithmetic error. Recompute that one substitution — the usual suspect is a sign slip when multiplying by a negative.

Worked examples

Try one yourself

Common questions