GCSE · Straight-line graphs

Finding the equation of a lineExam-style questions

How gradient + one point pins down a unique line, why c comes from substituting the point, and why disguised forms like 2y = 6x + 4 must be rearranged before reading anything off.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A straight line has equation $x + 2y = 8$

(a) Find the gradient of the line.

(b) Write down the coordinates of the point where the line crosses the $y$ -axis.
Level 5 · 3 marksTry it
2
A straight line crosses the $x$ -axis at $(4, 0)$ and the $y$ -axis at $(0, 6)$ .

Find the equation of the line.
Level 5 · 3 marksTry it
3
The diagram shows the line segment $PQ$ and the straight line $L$ . $P$ is the point $(-4, 9)$ and $Q$ is the point $(8, 1)$

$R$ is the point on $PQ$ such that $PR : RQ = 3 : 1$

$L$ passes through $R$ and has gradient $2$

Show that $L$ crosses the $y$ -axis at the point $(0, -7)$

(5 marks)
Level 5 · 5 marksTry it