Choose a spread of $x$-values (usually given in the question, e.g. $x = -2$ to $3$), then substitute each into the equation to get the matching $y$-value. For $y = 3x + 2$:

Plot each $(x, y)$ pair as a point, then join them with a single, ruled, straight line extending across the full grid — not just dot-to-dot between the plotted points. If one plotted point doesn't sit on the same line as the rest, you've made an arithmetic error and should recheck that value.

Some equations are given implicitly, e.g. $3x + 2y = 5$. Rearrange for $y$ first so you can substitute cleanly:

Then build the table exactly as before. Choosing $x$-values that are multiples of the denominator (here, even numbers) often keeps the $y$-values as whole numbers or simple fractions, which makes plotting far less error-prone.

If the question doesn't specify a range, pick values that keep the table manageable and centred near the origin — typically five or six integers such as $x = -2, -1, 0, 1, 2, 3$. Avoid huge values that would force an awkwardly-scaled grid; the goal is a clear, evenly-spaced set of points that reveal the line's direction.

An equation like $y = 4$ has the same $y$-value for every $x$, so it's a horizontal line through $4$ on the $y$-axis — no table is even needed. Likewise $x = -2$ is a vertical line through $-2$ on the $x$-axis. These are easy to lose marks on if you try to force them into a sloped-line table by mistake.

Draw the graph of $y = 7 - 4x$ for $-1 \leqslant x \leqslant 3$.

1. Substitute each integer $x$ from $-1$ to $3$:

$x=-1: y = 7-4(-1) = 11$

$x=0: y = 7$

$x=1: y = 3$

$x=2: y = -1$

$x=3: y = -5$

1. Plot $(-1,11), (0,7), (1,3), (2,-1), (3,-5)$.
2. Draw one ruled straight line through all five points, extending slightly beyond the first and last point.

Draw the graph of $2x + 3y = 6$ for $-3 \leqslant x \leqslant 3$.

1. Rearrange for $y$: $3y = 6 - 2x \implies y = \dfrac{6-2x}{3}$.
2. Choose multiples of $3$ to keep $y$ a whole number: $x=-3: y = \dfrac{12}{3}=4$; $x=0: y=2$; $x=3: y=0$.
3. Plot $(-3,4), (0,2), (3,0)$ and draw one ruled line through them, extending across the grid.