Equation of a Straight Line (Edexcel A Level Maths: Pure): Exam Questions

The straight line $L$ is parallel to the straight line with equation $2x+y-5=0$, and passes through the point $\left(1,1\right)$.

Find the equation of $L$.

The straight line $L$ is perpendicular to the straight line with equation $y-\frac{1}{3}x+\frac{2}{3}=0$, and passes through the origin.

Find the equation of $L$.

The straight line $l$ passes through the points (3, 4) and (9, 2).

Find the equation of $l$, giving your answer in the form $y=mx+c$.

Write down the gradient of a line perpendicular to $l$.

Find the equation of the straight line that passes through the points (-2, 3) and (3, 7).

Give your answer in the form

$ax+by+c=0$

where $a$, $b$ and $c$ are integers to be found.

Find the equation of the straight line parallel to $y=2x+3$, that passes through the point (3, 12).

Give your answer in the form $y=mx+c$.

The coordinates of the endpoints of a diameter of a circle are (-3, 5) and (3, -3).

Find the length of the diameter.

Find the coordinates of the centre of the circle.

Three points $A$, $B$ and $C$, have coordinates (-5,-11), (1, 1) and (4, 7) respectively.

Find the gradient of the line segment $AB$.

Find the gradient of the line segment $BC$.

Determine whether the line segments $AB$ and $BC$ are parallel or perpendicular.

Determine whether the line segments $AB$and $BC$ lie along the same straight line.

A dog breeder is measuring the rate at which a puppy grows by measuring its back length, the distance from the base of the neck to the base of the tail.

• At 2 weeks old, the puppy's back length measured 5 cm.

• Six weeks later, the puppy’s back length had increased by 4.2 cm.

Find a linear model that links $L$, the back length of the puppy in cm, to $w$, the age of the puppy in weeks.

Use the model to determine the back length of the puppy at birth.

Use the model to find the age of a puppy that has a back length of 23.9 cm.

This particular breed of dog is fully grown after 40 weeks.

Find the back length of the puppy at 40 weeks and comment on the suitability of the linear model beyond 40 weeks.

The line $l$ has equation$2x-y+3=0$.

$l$ crosses the $x$-axis at point $A$ and crosses the $y$-axis at point $B$.

Find the coordinates of points $A$ and $B$.

Hence, find the area of the triangle $OAB$, where $O$ is the origin.

A straight line passing through the origin $O$, is perpendicular to the straight line with equation $x+y=16$.

The two lines meet at the point $R$.

Find the coordinates of $R$.

$P$ is a point such that $OP:PR=3:1$

Find the coordinates of $P$.

Straight lines $l_1$ and $l_2$ are both parallel to the straight line with equation $3x-y+4=0$.

• $l_1$ passes through the origin

• $l_2$ passes through the point (-4, 7). 

Find the equations of $l_1$and $l_2$, giving your answers in form $y=mx+c$.

The line $l$ passes through the points (4, 2) and (8, 5).

Find the equation of the line $l$, giving your answer in the form $ax+by+c=0$
where $a$,$b$ and $c$ are integers to be found.

The line segment $AB$ is the diameter of a circle.

$A$has coordinates (-7,-9) and $B$ has coordinates (9, 3).

Find the coordinates of the centre of the circle and the length of the diameter.

Three points $A$, $B$ and $C$, have coordinates (-8, 1), (4, 4) and (12, 6) respectively.

Find the gradients of the line segments $AB$ and $BC$.

Determine whether the line segments $AB$ and $BC$ lie along the same straight line.

Find the equation of the straight line perpendicular to $2x+3y-4=0$that passes through the point (-1, -1).

Give your answer in the form $ax+by+c=0,$ where $a$, $b$ and $c$ are integers.

Three points $A$, $B$ and $C$, have coordinates (-4,-16), (2, 5) and (10, 33) respectively.

Show that $A$, $B$ and $C$ lie on the same straight line.

The line $l_1$ has equation $y=\frac{3}{5}x+6$

The line $l_2$ is perpendicular to $l_1$ and passes through the point $B\left(8,0\right)$, as shown in the sketch in Figure 4.

Show that an equation for line $l_2$ is

$5x+3y=40$

Given that

• lines $l_1$ and $l_2$ intersect at the point $C$

• line $l_1$ crosses the $x$-axis at the point $A$

find the exact area of triangle $ABC$, giving your answer as a fully simplified fraction in the form $\frac{p}{q}$

The distance a particular car can travel in a journey starting with a full tank of fuel was investigated.

• From a full tank of fuel, 40 litres remained in the car’s fuel tank after the car had travelled 80 km

• From a full tank of fuel, 25 litres remained in the car’s fuel tank after the car had travelled 200 km

Using a linear model, with $V$ litres being the volume of fuel remaining in the car’s fuel tank and $d$ km being the distance the car had travelled, find an equation linking $V$ with $d$.

Given that, on a particular journey

• the fuel tank of the car was initially full

• the car continued until it ran out of fuel

find, according to the model,

(i) the initial volume of fuel that was in the fuel tank of the car,

(ii) the distance that the car travelled on this journey.

In fact the car travelled 320 km on this journey.

Evaluate the model in light of this information.

The line $l_1$ has equation $3x-2y+4=0$ and crosses the $x$-axis at point $A$.

The line $l_2$ has equation $y=5-x$ and crosses the $y$-axis at point $B$.

Find the area of the triangle $OAB$, where $O$ is the origin.

Two perpendicular lines $l_1$ and $l_2$ intersect at point $P\left(2,5\right)$.

$l_2$ crosses the $x$-axis at point $Q\left(-3,0\right)$.

Find an equation of $l_1$, giving your answer in the form $y=a+bx$.

The points of intersection of the following straight lines form a parallelogram.

Find the coordinates of all four vertices of the parallelogram.

$\begin{array}{rcl}2y& =& 3x+12\\ & & \\ 2y& =& 8-x\end{array}$      $\begin{array}{rcl}3x-2y-12& =& 0\\ \frac{1}{2}x+y+2& =& 0\end{array}$

The line $l_1$ has equation $5x-2y+12=0$.

The line $l_2$ has equation $2x+5y+28=0$.

Determine if the lines $l_1$ and $l_2$ are parallel, perpendicular, or neither.

$l_1$ and $l_2$ intersect at the point $P$.

Find the coordinates of $P$.

$l_1$ meets the $y$-axis at the point $Q$.

Point $R$ lies on the line $PQ$ such that $PR:RQ$ =3 :1.

Find the coordinates of $R$.

The line $l$ passes through the points $\left(p,2p\right)$ and $\left(3p,9p\right)$.

Find an equation for the line $l$.

The line $l$ intersects the $y$-axis at the point (0, 3).

Find the value of $p$.

A line segment $AB$ is tangent to a circle at point $M$.

The endpoints of $AB$ have coordinates (-5, 16) and (5, 14).

$M$ is the midpoint of $AB$.

The line $MN$ is a diameter of the circle.

$N$ has coordinates (-4, -5).

Find the coordinates of the centre of the circle, $C$.

Find also the area of the circle, giving your answer to 3 significant figures.

The line $l_1$ has equation $3x-2y+10=0$ and crosses the $x$-axis at the point $A$.

The line $l_2$ is perpendicular to $l_1$ and crosses the $x$-axis at (9, 0).

$l_2$ crosses the $y$-axis at point $B$.

Find the area of the triangle $OAB$, where $O$ is the origin.

VAT is a tax that is added to goods and services.

A plumber charges a fixed fee of £27.50, plus £21 per hour. The plumber then charges VAT on top of the total cost, at a rate of 20%.

Let $P$ be the amount of money made by the plumber after $h$ hours of work.

Find a linear model that links $P$ and $h$.

A rival plumber charges a fixed fee of £37.80, plus £24 per hour. These prices already include VAT.

Find the number of hours for which both plumbers would charge the same amount.

A quadrilateral has four vertices with coordinates (-1, 6), (-3, 2), (0, -4) and (2, 0).

Find the equation for each of the four lines that form the quadrilateral.

State the mathematical name of the quadrilateral formed.

Two perpendicular lines intersect at (-4,-4). One of the lines also passes through the point (0, 6), the other passes through the point (0,-5.6).

A kite is formed by these two lines and two others. The kite has a line of symmetry along the $y$-axis. 

Find the area of the kite.

The tangent to a circle passes through the points $A\left(-8,-1\right)$ and $B\left(16,7\right)$.

The tangent touches the circle at the point $N$, where $AN:NB=5:3$.

Find the equation of the straight line along which the diameter of the circle at point $N$ lies.

Give your answer in the form $ax+by+c=0$, where $a$, $b$ and $c$are integers to be found.