1. Choose several $x$-values across the given range.
2. Substitute each into the equation to find the matching $y$-value.
3. Plot each $(x,y)$ pair as a point.
4. Use a ruler to draw one continuous straight line through every point, extending it to the edges of the grid.

$y=-2x+5$ for $-1 \leqslant x \leqslant 3$: substituting each $x$-value gives

If one plotted point doesn't line up with the rest once they're all marked on the grid, that's a strong signal a substitution error was made for that particular $x$-value — recheck that one calculation rather than assuming the ruler was drawn incorrectly.

1. Plot the $y$-intercept, $(0,c)$.
2. Use the gradient $m=\dfrac{\text{rise}}{\text{run}}$ to step to a second point.
3. Rule a straight line through both points, extending it across the full grid.

Draw $y=\dfrac{1}{2}x-1$: plot the intercept $(0,-1)$. Since $m=\tfrac12$ means "$1$ up for every $2$ across", step from $(0,-1)$ to reach $(2,0)$, then rule the line through both points. For extra accuracy, it's worth stepping out to a third point further along — e.g. $(4,1)$ — and checking all three lie on the same ruled line before extending it fully.

A straight line should always be extended as far as the grid allows in both directions, not stopped at the two points originally used to draw it — a "line segment" that only spans between two plotted points isn't a full graph of the equation, and can cost accuracy marks if the question later asks for a value outside that narrow section.

Complete the table below for $y=3x-2$, then describe how the graph would be drawn.

Solution

Substitute each $x$-value: $x=-2$ gives $y=3(-2)-2=-8$; $x=0$ gives $y=-2$; $x=2$ gives $y=4$.

Plot $(-2,-8)$, $(0,-2)$ and $(2,4)$, then use a ruler to draw a single straight line through all three points, extending it to the edges of the grid — a line stopped short at the plotted points, or joined freehand, both lose accuracy marks.