Linear Graphs (Edexcel GCSE Maths: Higher): Exam Questions

On the grid, draw the graph of  for values of  from 

On the grid, draw the graph of  for values of from 

The equation of the line is 
The equation of the line  is 

Show that these two lines are parallel.

and are parallel lines.

The equation of is 
passes through the point  .

Find an equation for .

The diagram shows a straight line, , drawn on a grid.

A straight line, , is parallel to the straight line and passes through the point .
Find an equation of the straight line .

is a line segment.

The midpoint of the line segment has coordinates (3, 5)
Point has coordinates (9, 2)

Work out the coordinates of point .

Work out an equation of the straight line that passes through (9, 2) and (3, 5)

The line  has equation 

Find the gradient of .

The line is perpendicular to and passes through the point (3, 1).

Find the equation of in the form , where and are constants.

The straight line  has equation 

The straight line  passes through the points  and 
Michael says that the lines  and  are perpendicular.

Is Michael correct?
You must show clearly how you get your answer.

The straight line has equation 

The straight line  is perpendicular to  and passes through the point (9 , -1)

Find an equation for 
Give your answer in the form 

The graph shows two parallel lines, Line A and Line B.

Line A has equation .
Line B passes through the point (4, 26).

Find the equation of Line B.

A straight line passes through the point (0, 6) and is perpendicular to  y = 4x − 5.

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

Point A has coordinates (-4, 6) and point B has coordinates (8, 3).

i) Find the gradient of line AB.

[2]

ii) Find the equation of line AB.

[2]

Point P has coordinates (0, -2).

Write down the equation of the line parallel to line AB that passes through P.

Show that line 3y = 4x − 14 is perpendicular to line 4y = −3x + 48.

The equation of a straight line is   

Circle the point where the line crosses the -axis.

A straight line

has gradient 6
and
passes through the point (3, 19)

Work out the equation of the line.
Give your answer in the form

Jim buys a plant of height 20 cm.

The graph shows how the height of the plant changes during the next 4 days.

Work out a formula for in terms of .

The line is drawn below.

Find an equation of the line perpendicular to line that passes through the point (0, 1).

The straight line has equation 

Find an equation of the straight line perpendicular to  that passes through (-8, 3).

The straight line has the equation  The point has coordinates (3, —5)

Find an equation of the straight line that is perpendicular to and passes through .

Find an equation of the line that passes through and is perpendicular to .

The line has equation 

Show that the point  lies on .

Find an equation of the line perpendicular to , which passes through . Give your answer in the form , where and are integers.

The line has equation
The line is perpendicular to and passes through the point .

Find an equation for in the form , where  and are integers.

The line  crosses the -axis at the point and the -axis at the point .

Find the -coordinate of and the -coordinate of .

Given that is the origin,

find the area of the triangle .

The points and  have coordinates  and  respectively. 

The line  is perpendicular to  and passes through the midpoint of 

Find an equation for 

is the point with coordinates 

is the point with coordinates 
The straight line goes through both and .

Is the line with equation  perpendicular to line ? You must show how you got your answer.

The straight line passes through the points (4, −1) and (6, 4)

The straight line is perpendicular to and intersects the -axis at the point (0, 8)

Find the coordinates of the point where intersects the -axis.

is a rhombus.

The diagonals,  and , intersect at the point .
The coordinates of  are 

The points  and  both lie on the line with equation

Find the exact coordinates of the point where the line through  and  intersects the .

P is the point (0, -1) and Q is the point (5, 9).

Find the equation of the line through P that is perpendicular to the line PQ.

Here is line L and the graph of

The scales of the axes are not shown.

Work out the equation of line L.

Show that the lines  and  are parallel.

Do not use a graphical method.

Is the point (–5, –6) above, below or on the line  ?

Tick one box.

Above    Below   On the line

You must show your working.
Do not use a graphical method.

Figure 1

The line has equation

Find the gradient of .

The line crosses the -axis at the point and the -axis at the point , as shown in Figure 1.

The line is perpendicular to and passes through .

Find an equation of .

The line crosses the -axis at the point .

Find the area of triangle .

 is a rhombus.
The coordinates of are
The equation of the diagonal is 
Find an equation of the diagonal .

Figure 2

The line , shown in Figure 2 has equation 
The line passes through the origin and is perpendicular to 

Find an equation for the line

The line intersects the line at the point . Line crosses the -axis at the point as shown in Figure 2.

Find the area of triangle .

Give your answer in the form , where and are integers to be determined.

The point has coordinates 
The point has coordinates 

A line perpendicular to is given by the equation 

Find an expression for in terms of .

 is a square.
and  are points on the -axis.
is a point on the -axis.
 is a straight line.

The equation of the line that passes through the points and is 
Find the length of .

(—2, 1), (6, 5) and (4, ) are the vertices of a right-angled triangle .
Angle is the right angle.

Find an equation of the line that passes through and .
Give your answer in the form  where , and are integers.

The points  and have coordinates (3, 4) and (7, —6) respectively. The straight line passes through and is perpendicular to . Find an equation for , giving your answer in the form , where  and  are integers.

is a rectangle.

 and are points on the straight line with equation  and  are points on the straight line .

Find an equation for .

is an isosceles triangle with

is the point with coordinates (–1, 5)
is the point with coordinates (2, 10)
is the midpoint of .

Find an equation of the line through the points and .
Give your answer in the form where  and are integers.

and are two straight lines. The origin of the coordinate axes is .

has equation 
is perpendicular to  and passes through the point with coordinates (8, 6)

crosses the -axis at the point .
intersects the straight line with equation  at the point .

Find the area of triangle .
Show your working clearly.

The straight line passes through point (– 6, 2) and point (5, 3)
The straight line is perpendicular to and passes through the midpoint of and .
The line intersects the line at point .

Calculate the area of triangle .

Line A has equation

Line B is

perpendicular to line A
and
passes through the point (8, 5)

Work out the coordinates of the point where line B intersects the -axis.