Mathematics 0580 · IGCSE
Equations of linear graphs
56 practice questions on Equations of linear graphs, with worked solutions and instant marking.
A straight line $l$ appears on the coordinate grid.
Feb/March 2017
A straight line labelled $l$ is plotted on a set of $x$- and $y$-axes.
Feb/March 2017
On a 1 cm$^2$ grid, the diagram shows point $P$, shape $S$ and lines $A$ and $B$.
Feb/March 2021
A lies at $(0,4)$ and B lies at $(8,0)$. $L_1$ runs parallel to the $x$-axis. $L_2$ goes through A and B.
Feb/March 2023
The lines $y = 2x - 5$ and $y = 3$ meet at point $P$.
Feb/March 2024
$A$ is the point $(6, 1)$ while $B$ is the point $(2, 7)$.
Feb/March 2024
The line $y = 2x - 5$ meets the line $y = 3$ at the point $P$.
Feb/March 2024
The grid shows line $L$.
Feb/March 2025
State the coordinates of the point at which the graph of $y = 5x - 3$ intersects the $y$-axis.
Feb/March 2025
The straight line $l$ is drawn passing through $(0,3)$ and $(4,11)$.
May/June 2015
The line $AB$ is plotted on the grid, with point $A$ positioned at about $(0.5, 1)$ and point $B$ at $(3, 7)$.
May/June 2016
The equation for line $L$ is $y = 4x - 3$.
May/June 2016
On a grid, the straight line $L$ has been drawn.
May/June 2016
A grid is displayed, with a straight line marked $L$ running across it.
May/June 2016
The straight line connects the points $A(-2, -5)$ and $B(4, 13)$.
May/June 2016
Line $l$ is given by the equation $y = 4x - 6$.
May/June 2017
The point $A$ is $(-2, 0)$ and the point $B$ is $(0, 4)$. A coordinate grid with the $x$- and $y$-axes labelled is shown. The sketch is marked NOT TO SCALE.
May/June 2017
The points A(-3, 8) and B(2, -2) are connected by a line.
May/June 2017
Four inequalities define the region $R$. One of them is $y \le x + 1$. On a coordinate grid, region $R$ is shaded.
May/June 2018
Calculate the angle made by line $AB$ with the $x$-axis.
May/June 2018
Find the equation of the straight line perpendicular to the line $y = \frac{1}{2}x + 1$ that goes through the point $(1, 3)$.
May/June 2018
The diagram depicts a point $P$ and a line $L$ on a coordinate grid whose axes are labelled $x$ and $y$. Point $P$ is shown at about $(-3, -1)$. Line $L$ slopes upwards from the lower left to the upper right.
May/June 2019
Determine the co-ordinates of the point where the line $y = 3x - 8$ meets the y-axis.
May/June 2019
State the co-ordinates of the point at which the line $y = 6x - 3$ meets the $y$-axis.
May/June 2019
Work out the gradient of this line.
May/June 2019
Determine the equation of line $AC$ in the form $y=mx+c$.
May/June 2019
A coordinate plane is displayed with a straight line marked $L$. The x-axis runs from $-4$ to $6$, and the y-axis runs from $-2$ to $5$.
May/June 2021
A straight-line graph of $l$ is shown on the coordinate axes.
May/June 2021
The sketch presents a line L together with points A and B on a grid. Both axes are labelled, and A lies on the line to the left of the y-axis, while B is on the line at about (6,1).
May/June 2021
A line $L$ is drawn on the grid.
May/June 2022
State the coordinates of the point at which the line $y = 3x - 5$ intersects the $y$-axis.
May/June 2024
A is the point $(0, 2)$, while B is the point $(8, 6)$.
May/June 2024
Find the coordinates for the midpoint of $AB$.
May/June 2024
Six graphs, A, B, C, D, E and F, are displayed. Each one has $x$- and $y$-axes, with tick marks at 3 on each axis where indicated. Graph E contains a vertical line drawn at $x = 3$. The remaining graphs each show different straight lines.
May/June 2025
The equation of line $L$ is $y = 2(x - 5)$.
May/June 2025
The diagram displays a straight line $l$. It meets the $y$-axis at about $y=2$ and passes through the point near $(6,5)$.
Oct/Nov 2017
State the coordinates of point $A$.
Oct/Nov 2018
A coordinate grid displays line $l$ together with points $A$ and $B$.
Oct/Nov 2018
On the grid, the line $L$ is plotted. The $x$-axis runs from $-4$ to $4$, while the $y$-axis runs from $-5$ to $5$. Line $L$ passes through $(0,1)$ and slopes upwards to the right.
Oct/Nov 2019
The line $L$ appears on the grid.
Oct/Nov 2019
A straight line connects $A(1,3)$ with $B(5,8)$.
Oct/Nov 2019
A graph with axes marked $x$ and $y$ shows a line named $L$.
Oct/Nov 2020
A coordinate grid is displayed, with the $x$-axis and $y$-axis labelled. Point $A$ appears on the grid, and a straight line $L$ crosses the grid.
Oct/Nov 2020
The coordinate axes are labelled $x$ and $y$, and a straight line marked L is drawn on the graph.
Oct/Nov 2021
Find the equation of the line joining $A$ and $B$. Write your answer in the form $y = mx + c$.
Oct/Nov 2021
Determine the equation of the straight line. Write your answer in the form $y = mx + c$.
Oct/Nov 2021
The diagram represents a straight line $L$ on axes marked $x$ and $y$, and it goes through the origin.
Oct/Nov 2022
A kite is shown on a coordinate grid. Its diagonals meet at the point $(-2, -5)$. One of the diagonals is given by $y = 4x + 3$.
Oct/Nov 2022
Work out the vector $4a$.
Oct/Nov 2022
Point A and line $L$ are displayed on the grid.
Oct/Nov 2023
A coordinate grid displays the straight line labelled $L$.
Oct/Nov 2023
The coordinates of A are $(0,2)$, those of B are $(3,3)$ and those of C are $(4,0)$.
Oct/Nov 2023
The grid shows the line L.
Oct/Nov 2025
Find the equation of line L in the form $y=mx+c$.
Oct/Nov 2025
Line L is shown on the grid.
Oct/Nov 2025
Determine the equation of the straight line through the points (2,0) and (0,4). State your answer in the form $y=mx+c$.
Oct/Nov 2025