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47 questions at your level
Difficulty
All
Level 1
Level 2
Level 3
Level 4
Level 5
Gradient and intercept
13 questions
Lesson
Not started
Mark as done
A line has equation
y
=
4
x
−
1
y = 4x - 1
y
=
4
x
−
1
. Write down
(a)
its gradient,
(b)
its
y
y
y
-intercept.
●
●●●●
Level 1
2 marks
Start
→
Mark as done
The gradient of the line
2
y
=
6
x
−
4
2y = 6x - 4
2
y
=
6
x
−
4
is
Circle your answer.
A
6
6
6
B
3
3
3
C
−
4
-4
−
4
D
−
2
-2
−
2
●
●●●●
Level 1
1 mark
Start
→
Mark as done
A
A
A
is the point
(
−
2
,
3
)
(-2, 3)
(
−
2
,
3
)
and
B
B
B
is the point
(
4
,
11
)
(4, 11)
(
4
,
11
)
.
(a)
Work out the length of
A
B
AB
A
B
. [3]
(b)
Work out the gradient of the line
A
B
AB
A
B
. [1]
●●
●●●
Level 2
4 marks
Start
→
Mark as done
Work out the gradient of the straight line passing through the points
(
1
,
2
)
(1, 2)
(
1
,
2
)
and
(
4
,
11
)
(4, 11)
(
4
,
11
)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
A straight line has equation
y
=
5
−
2
x
y = 5 - 2x
y
=
5
−
2
x
(a)
Write down the gradient of the line.
(b)
Write down the coordinates of the point where the line crosses the
y
y
y
-axis.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Work out the gradient of the straight line passing through the points
(
3
,
−
1
)
(3, -1)
(
3
,
−
1
)
and
(
7
,
7
)
(7, 7)
(
7
,
7
)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
A straight line has equation
y
=
7
−
4
x
y = 7 - 4x
y
=
7
−
4
x
(a)
Write down the gradient of the line.
(b)
Write down the coordinates of the point where the line crosses the
y
y
y
-axis.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Work out the gradient of the straight line passing through the points
(
2
,
5
)
(2, 5)
(
2
,
5
)
and
(
6
,
−
3
)
(6, -3)
(
6
,
−
3
)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Work out the gradient of the straight line passing through the points
(
−
2
,
7
)
(-2, 7)
(
−
2
,
7
)
and
(
4
,
−
5
)
(4, -5)
(
4
,
−
5
)
●●●●
●
Level 4
2 marks
Start
→
Mark as done
The line
L
L
L
has equation
y
=
3
x
+
2
y = 3x + 2
y
=
3
x
+
2
(a)
Show that the point
(
5
,
17
)
(5, 17)
(
5
,
17
)
lies on
L
L
L
.
(b)
Find the coordinates of the point where
L
L
L
crosses the
x
x
x
-axis.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
The straight line
y
=
m
x
+
c
y = mx + c
y
=
m
x
+
c
passes through the points
(
0
,
−
2
)
(0, -2)
(
0
,
−
2
)
and
(
4
,
6
)
(4, 6)
(
4
,
6
)
.
Find the values of
m
m
m
and
c
c
c
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
The straight line through the points
(
2
,
k
)
(2, k)
(
2
,
k
)
and
(
5
,
13
)
(5, 13)
(
5
,
13
)
has gradient 4.
Work out the value of
k
k
k
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
Show that the points
A
(
−
2
,
1
)
A(-2, 1)
A
(
−
2
,
1
)
,
B
(
1
,
7
)
B(1, 7)
B
(
1
,
7
)
and
C
(
3
,
11
)
C(3, 11)
C
(
3
,
11
)
lie on the same straight line.
●●●●●
Level 5
3 marks
Start
→
Finding the equation of a line
16 questions
Lesson
Not started
Mark as done
A line has gradient
2
2
2
and passes through
(
0
,
5
)
(0, 5)
(
0
,
5
)
. Write down its equation.
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Write down the equation of the line that is parallel to the
x
x
x
-axis and passes through
(
3
,
−
2
)
(3, -2)
(
3
,
−
2
)
.
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Does the point
(
4
,
9
)
(4, 9)
(
4
,
9
)
lie on the line
y
=
2
x
+
1
y = 2x + 1
y
=
2
x
+
1
? Show how you decide.
●
●●●●
Level 1
1 mark
Start
→
Mark as done
A line passes through
(
0
,
1
)
(0, 1)
(
0
,
1
)
and
(
2
,
7
)
(2, 7)
(
2
,
7
)
. Find its equation.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
Write down the equation of the straight line with gradient 2 that passes through the point
(
0
,
−
3
)
(0, -3)
(
0
,
−
3
)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Write down the equation of the straight line with gradient
4
4
4
that passes through the point
(
0
,
1
)
(0, 1)
(
0
,
1
)
●●●
●●
Level 3
1 mark
Start
→
Mark as done
A
B
C
ABC
A
B
C
is a straight line.
A (−3, 5)
B (3, 1)
C
O
x
y
Point
A
A
A
has coordinates
(
−
3
,
5
)
(-3, 5)
(
−
3
,
5
)
Point
B
B
B
has coordinates
(
3
,
1
)
(3, 1)
(
3
,
1
)
B
C
=
3
2
A
B
BC = \frac{3}{2}AB
B
C
=
2
3
A
B
Find the coordinates of point
C
C
C
.
(3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Find the equation of the straight line with gradient
−
3
-3
−
3
that passes through the point
(
2
,
5
)
(2, 5)
(
2
,
5
)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
The diagram shows the straight line
L
L
L
.
-2
-1
1
2
3
4
5
-2
2
4
6
8
10
12
14
(1, 5)
(3, 11)
L
x
y
Diagram NOT accurately drawn
The points
(
1
,
5
)
(1, 5)
(
1
,
5
)
and
(
3
,
11
)
(3, 11)
(
3
,
11
)
lie on
L
L
L
.
Find the equation of
L
L
L
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A straight line has equation
2
y
=
6
x
+
4
2y = 6x + 4
2
y
=
6
x
+
4
Write down the gradient of the line.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Find the equation of the straight line with gradient
−
2
-2
−
2
that passes through the point
(
3
,
4
)
(3, 4)
(
3
,
4
)
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Find the equation of the straight line passing through the points
(
2
,
3
)
(2, 3)
(
2
,
3
)
and
(
6
,
11
)
(6, 11)
(
6
,
11
)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A straight line has equation
3
y
=
9
x
−
6
3y = 9x - 6
3
y
=
9
x
−
6
(a)
Write down the gradient of the line.
(b)
Write down the coordinates of the point where the line crosses the
y
y
y
-axis.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
A straight line has equation
x
+
2
y
=
8
x + 2y = 8
x
+
2
y
=
8
(a)
Find the gradient of the line.
(b)
Write down the coordinates of the point where the line crosses the
y
y
y
-axis.
●●●●●
Level 5
3 marks
Start
→
Mark as done
A straight line crosses the
x
x
x
-axis at
(
4
,
0
)
(4, 0)
(
4
,
0
)
and the
y
y
y
-axis at
(
0
,
6
)
(0, 6)
(
0
,
6
)
.
Find the equation of the line.
●●●●●
Level 5
3 marks
Start
→
Mark as done
A
B
D
L
O
x
y
In the diagram
A
A
A
is the point
(
0
,
10
)
(0, 10)
(
0
,
10
)
B
B
B
is the point
(
15
,
0
)
(15, 0)
(
15
,
0
)
D
D
D
is the point on
A
B
AB
A
B
such that
A
D
:
D
B
=
2
:
3
AD : DB = 2 : 3
A
D
:
D
B
=
2
:
3
The line
L
L
L
passes through
D
D
D
.
The gradient of
L
L
L
is
2.5
2.5
2.5
L
L
L
passes through the point with coordinates
(
−
3
,
f
)
(-3, f)
(
−
3
,
f
)
Show that
f
<
−
16
f < -16
f
<
−
16
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Parallel and perpendicular lines
18 questions
Lesson
Not started
Mark as done
Write down the equation of a line parallel to
y
=
3
x
+
2
y = 3x + 2
y
=
3
x
+
2
that passes through
(
0
,
−
4
)
(0, -4)
(
0
,
−
4
)
.
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Which of these lines is parallel to
y
=
2
x
−
5
y = 2x - 5
y
=
2
x
−
5
?
\quad
A:
y
=
5
x
−
2
y = 5x - 2 \qquad
y
=
5
x
−
2
B:
y
=
2
x
+
7
y = 2x + 7 \qquad
y
=
2
x
+
7
C:
y
=
−
2
x
−
5
y = -2x - 5
y
=
−
2
x
−
5
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Line L has equation
y
=
5
x
+
1
y = 5x + 1
y
=
5
x
+
1
. Line M is parallel to L. Write down the gradient of M.
●
●●●●
Level 1
1 mark
Start
→
Mark as done
A line is parallel to
y
=
−
x
+
6
y = -x + 6
y
=
−
x
+
6
and passes through
(
0
,
2
)
(0, 2)
(
0
,
2
)
. Write down its equation.
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Are the lines
y
=
4
x
+
3
y = 4x + 3
y
=
4
x
+
3
and
2
y
=
8
x
−
1
2y = 8x - 1
2
y
=
8
x
−
1
parallel? Explain your answer.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
Write down the equation of the straight line that is parallel to
y
=
−
3
x
+
2
y = -3x + 2
y
=
−
3
x
+
2
and passes through the point
(
0
,
−
5
)
(0, -5)
(
0
,
−
5
)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Line
L
L
L
has equation
y
=
−
1
2
x
+
3
y = -\tfrac{1}{2}x + 3
y
=
−
2
1
x
+
3
(a)
Find the equation of the line perpendicular to
L
L
L
that passes through the point
(
2
,
7
)
(2, 7)
(
2
,
7
)
. (3 marks)
(b)
Does the point
(
10
,
23
)
(10, 23)
(
10
,
23
)
lie on the line you found in part (a)? Show how you decide. (1 mark)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
Write down the equation of the straight line that is parallel to
y
=
2
x
−
1
y = 2x - 1
y
=
2
x
−
1
and passes through the point
(
0
,
7
)
(0, 7)
(
0
,
7
)
●●●●
●
Level 4
2 marks
Start
→
Mark as done
The line
L
L
L
has equation
y
=
4
x
−
3
y = 4x - 3
y
=
4
x
−
3
Write down the gradient of a line
perpendicular
to
L
L
L
.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
The line
L
L
L
has equation
y
=
1
2
x
+
4
y = \tfrac{1}{2}x + 4
y
=
2
1
x
+
4
(a)
Write down the gradient of a line perpendicular to
L
L
L
.
(b)
Find the equation of the line perpendicular to
L
L
L
that passes through the point
(
2
,
1
)
(2, 1)
(
2
,
1
)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Line
A
A
A
has equation
y
=
2
x
+
1
y = 2x + 1
y
=
2
x
+
1
Line
B
B
B
has equation
2
y
=
4
x
−
3
2y = 4x - 3
2
y
=
4
x
−
3
Are lines
A
A
A
and
B
B
B
parallel? You must show your working.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
The straight line
L
1
L_1
L
1
has equation
3
y
=
12
x
−
5
3y = 12x - 5
3
y
=
12
x
−
5
The straight line
L
2
L_2
L
2
is perpendicular to
L
1
L_1
L
1
and passes through the point
(
8
,
1
)
(8, 1)
(
8
,
1
)
.
Find an equation of
L
2
L_2
L
2
.
Give your answer in the form
a
x
+
b
y
+
c
=
0
ax + by + c = 0
a
x
+
b
y
+
c
=
0
, where
a
a
a
,
b
b
b
and
c
c
c
are integers. (4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The equation of line
L
1
L_1
L
1
is
y
=
−
4
x
+
3
y = -4x + 3
y
=
−
4
x
+
3
The equation of line
L
2
L_2
L
2
is
8
y
+
k
x
−
3
=
0
8y + kx - 3 = 0
8
y
+
k
x
−
3
=
0
L
1
L_1
L
1
is perpendicular to
L
2
L_2
L
2
Find the value of
k
k
k
.
You must show all your working.
(3 marks)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Find the equation of the straight line that is perpendicular to
y
=
2
x
+
3
y = 2x + 3
y
=
2
x
+
3
and passes through the point
(
4
,
1
)
(4, 1)
(
4
,
1
)
●●●●●
Level 5
3 marks
Start
→
Mark as done
Show that the lines
y
=
3
x
−
2
y = 3x - 2
y
=
3
x
−
2
and
x
+
3
y
=
6
x + 3y = 6
x
+
3
y
=
6
are perpendicular.
●●●●●
Level 5
3 marks
Start
→
Mark as done
The line
L
1
L_1
L
1
has equation
y
=
5
−
2
x
y = 5 - 2x
y
=
5
−
2
x
The line
L
2
L_2
L
2
is parallel to
L
1
L_1
L
1
and passes through the point
(
3
,
4
)
(3, 4)
(
3
,
4
)
.
Find the coordinates of the point where
L
2
L_2
L
2
crosses the
y
y
y
-axis.
●●●●●
Level 5
3 marks
Start
→
Mark as done
Find the equation of the straight line that is perpendicular to
3
x
+
y
=
7
3x + y = 7
3
x
+
y
=
7
and passes through the point
(
3
,
2
)
(3, 2)
(
3
,
2
)
●●●●●
Level 5
3 marks
Start
→
Mark as done
The line
L
1
L_1
L
1
has equation
y
=
4
x
−
1
y = 4x - 1
y
=
4
x
−
1
The line
L
2
L_2
L
2
is perpendicular to
L
1
L_1
L
1
and passes through the point
(
8
,
0
)
(8, 0)
(
8
,
0
)
.
Find the coordinates of the point where
L
2
L_2
L
2
crosses the
y
y
y
-axis.
●●●●●
Level 5
3 marks
Start
→