Straight-line graphs: gradient, y = mx + c, parallel & perpendicular

Examiners found many candidates could not state what a gradient is: answers like $2.5x$ or $\tfrac{5}{2}x$ were common. The gradient is a single number, e.g. $m = 2.5$ — with no $x$ attached.

The perpendicular gradient is the negative reciprocal $-\dfrac{1}{m}$. Candidates gave $m = 2$ or $m = -2$ (right size, wrong sign, or no reciprocal) instead of flipping the fraction and changing the sign.

A line such as $x + y = 7$ must pass through $(7, 0)$ and $(0, 7)$; some started at 7 on one axis but joined to 8 on the other. Plot the intercepts exactly and join them with a ruler.

$x = k$ is a vertical line and $y = k$ is horizontal. Candidates drew $x = 2$ when $y = 2$ was wanted. The variable set equal to a number names the axis the line runs parallel to.

Rearrange before reading $m$. From $2y = 3x - 8$, divide by 2: $y = \dfrac{3}{2}x - 4$, so $m = \dfrac{3}{2}$ — not $3$. Reading the coefficient off an unrearranged line is a frequent slip.