Equations of linear graphs

On the grid, shade region $R$, defined by the inequalities $1\le x\le5$, $2\le y\le4$.

May/June 2015

Simplify the expression $\frac{4x-1}{3}+\frac{3x+5}{2}$.

May/June 2015

$A$ has coordinates $(0, 3)$, $B$ has coordinates $(1, 5)$ and $C$ has coordinates $(p, -1)$.

May/June 2017

The diagram displays a circle with centre $C(0,1)$. $P(3,5)$ lies on the circle's circumference.

May/June 2021

The equation of line $L$ is $2y = 5x + 3$.

May/June 2025

Points $A$, $B$ and $C$ have been drawn on the grid.

May/June 2025

Find the three inequalities that describe the unshaded region $R$.

May/June 2025

In the diagram, the line $3y + 2x = 13$ cuts the coordinate axes at $A$ and $B$.

Oct/Nov 2016

A straight line for $2y = x + 4$ has been plotted on the grid.

Oct/Nov 2018

The diagram depicts a triangle obtained by linking the points $A(1,2)$, $B(13,2)$ and $C(4,8)$. The equation for line $BC$ is $2x + 3y = 32$.

Oct/Nov 2020

The diagram displays a shaded region $ABC$. The equation for line $AC$ is $y = -\frac{1}{2}x + 5$.

Oct/Nov 2021

The diagram displays the points $A(0,6)$, $B(p,0)$ and $C(p,6)$. The line $AB$ has equation $3y + 4x = 18$.

Oct/Nov 2022

Line $L$ is represented by $4y = x - 5$. Find the gradient of line $L$.

Oct/Nov 2023

A shaded triangle $ABC$ is drawn on a $1$ cm square grid. For the side $AC$, the equation is $y=-\frac{3}{2}x+1$.

Oct/Nov 2024

Point A is $(3,-2)$, while point B is $(5,4)$.

Oct/Nov 2025

The equation for line L is $y=\frac{x}{5}+3$. The diagram shows lines L and M, the origin O, point A on the x-axis, and point B on the y-axis.

Oct/Nov 2025