� Tables of values
Substitute each \(x\)-value into the equation to find \(y\). Then you can plot the points with a ruler on squared paper.
� On the line?
A point lies on a line if its coordinates fit the equation. Substitute and check.
� Gradient from a graph
The rise-and-run triangle is drawn for you: gradient = how much up over how much across.
� Gradient — plotted points
No triangle this time — count the rise and run between the two marked points yourself.
� Gradient from coordinates
No picture at all — use \(m=\dfrac{y_2-y_1}{x_2-x_1}\), the same rise over run.
� Special lines
Horizontal lines have equations like \(y=5\). Vertical lines have equations like \(x=2\).
Key ideas
Table of values: substitute each \(x\) into the equation to find \(y\), plot the points, then draw one straight line through them with a ruler.
Gradient: \(m=\dfrac{\text{rise}}{\text{run}}\) — how much up over how much across, moving left to right.
Sign of the gradient: uphill left-to-right is positive; downhill is negative.
Horizontal lines (\(y=a\)) have gradient \(0\). Vertical lines (\(x=b\)) have an undefined gradient.