Coordinate geometry — straight-line graphs, gradient, parallel and perpendicular

Lines such as x + y = 7 were started correctly at 7 on one axis but joined to 8 on the other; x = 2 was drawn instead of y = 2.

Students gave m = 2 or m = −2 instead of the negative reciprocal, and forgot to rearrange the given equation into y = mx + c before reading the gradient.

Examiners were "surprised that many do not actually know what the gradient is" — values like 2.5x or 5/2x were commonly given. The gradient is a single numerical value.

Gradient is $\dfrac{\text{rise}}{\text{run}}$, the change in $y$ over the change in $x$. Turning it upside-down (run over rise) gives the reciprocal — e.g. reading $\tfrac{1}{2}$ where the true gradient is $2$.

Rearranging $3y = -2x + 12$ to $y = mx + c$, divide EVERY term by 3: $y = -\tfrac{2}{3}x + 4$. Dividing only the $x$-term and leaving $c$ as $12$ is a frequent slip.