Topics
3 Coordinate geometry
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Stage 5.1-2

3.02 The gradient of an interval

Lesson
Worksheet
Practice
Worksheet
Gradient from a graph
1

Describe the gradient of the lines in the following graphs:

a
-4
-3
-2
-1
1
2
3
4
x
-2
-1
1
2
3
4
5
6
7
8
9
y
b
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
d
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
2

For each of the following graphed lines:

i

Find the gradient.

ii

Find the y-intercept.

iii

Find the x-intercept.

a
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
b
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
3

State the gradient of any line parallel to the x-axis.

4

Consider the intervals AB and BC on the given graph:

a

Find the gradient of AB.

b

Find the gradient of BC.

1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
y
5

For each of the following intervals between points A and B:

i

Find the rise.

ii

Find the run.

iii

Find the gradient.

a

A \left(2, 4\right) and B \left(8, 6\right)

1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
y
b

A\left( - 3 , 4\right) and B\left(3, 16\right)

-4
-3
-2
-1
1
2
3
4
x
2
4
6
8
10
12
14
16
y
c

A \left( - 2 , - 1 \right) and B \left(2, - 13 \right)

-4
-3
-2
-1
1
2
3
4
x
-14
-12
-10
-8
-6
-4
-2
y
d

A \left( - 1 , 2\right) and B \left(1, - 4 \right)

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
e

A \left(1, 3\right) and B \left(7, - 3 \right)

1
2
3
4
5
6
7
x
-4
-3
-2
-1
1
2
3
4
y
f

A \left( - 3 , - 2 \right) and B \left(5, 6\right)

-4
-3
-2
-1
1
2
3
4
5
x
-4
-3
-2
-1
1
2
3
4
5
6
y
g

A \left(4, 4\right) and B \left(7, 7\right)

1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
7
8
y
h

A \left(2, 2\right) and B \left(6, 10\right)

1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
y
i

A \left(1, 5\right) and B\left(3, 1\right)

1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
y
j

A \left( - 8 , 4\right) and B \left( - 3 , 24\right)

-9
-8
-7
-6
-5
-4
-3
-2
-1
x
3
6
9
12
15
18
21
24
y
6

For each of the following lines with y-intercept Y and x-intercept X:

i

Find the rise using the intercepts.

ii

Find the run using the intercepts.

iii

Find the gradient of the interval XY.

a

Y \left(0, 5\right) and X \left( - 5 , 0\right)

-7
-6
-5
-4
-3
-2
-1
1
2
x
-2
-1
1
2
3
4
5
6
7
y
b

Y \left(0, 4\right) and X \left(2, 0\right)

-4
-3
-2
-1
1
2
3
4
5
x
-2
-1
1
2
3
4
5
6
7
y
c

Y \left(0, 9\right) and X \left( - 3 , 0\right)

-6
-5
-4
-3
-2
-1
1
2
3
x
-1
1
2
3
4
5
6
7
8
9
10
y
d

Y \left(0, 2\right) and X \left( - 6 , 0\right)

-7
-6
-5
-4
-3
-2
-1
1
2
x
-3
-2
-1
1
2
3
4
5
6
y
e

Y \left(0, 1\right) and X \left(5, 0\right)

-2
-1
1
2
3
4
5
6
7
x
-4
-3
-2
-1
1
2
3
4
5
y
f

Y \left(0, - 3 \right) and X \left(9, 0\right)

-1
1
2
3
4
5
6
7
8
9
10
x
-5
-4
-3
-2
-1
1
2
3
y
g

Y \left(0, - 14 \right) and X \left( - 7 , 0\right)

-8
-7
-6
-5
-4
-3
-2
-1
1
x
-16
-14
-12
-10
-8
-6
-4
-2
2
y
h

Y \left(0, 14\right) and X \left( - 2 , 0\right)

-5
-4
-3
-2
-1
1
2
3
x
-2
2
4
6
8
10
12
14
16
y
i

Y \left(0, 12\right) and X \left(6, 0\right)

-2
-1
1
2
3
4
5
6
7
x
-2
2
4
6
8
10
12
14
y
Gradient from a pair of coordinates
7

Find the gradient of the line that passes through the given points:

a

A \left(4, 3\right) and B \left(8, 15\right)

b

A \left(3, 5\right) and B \left(5, 1\right)

c

A \left(1, 3\right) and B \left(4, 4\right)

d

A \left(2, 4\right) and B \left(7, - 6 \right)

e

A \left( - 5 , - 3 \right) and B \left( - 2 , 12\right)

f

A \left( - 2 , 4\right) and B \left(2, 6\right)

8

Find the gradient, m, of the following lines.

a

A line that passes through Point A \left(3, - 9 \right) and the origin.

b

A line that passes through Point A \left( - 4 , 0\right) and Point B \left(0, 4\right).

c

A line that passes through Point A \left( - 2 , 4\right) and Point B \left(5, 1\right).

d

A line that passes through Point A \left( - 3 , - 1 \right) and Point B \left( - 5 , 1\right).

e

A line that passes through Point A \left(1, - 1 \right) and Point B \left(-1, - 2 \right).

9

Determine whether the following pairs of coordinates will have a gradient that is defined or undefined:

a

\left( - 10 , 5\right) and \left( - 10 , 12\right)

b

\left(10, 5\right) and \left(10, 1\right)

c

\left(10, - 1 \right) and \left( - 10 , - 1 \right)

d

\left( - 10 , 5\right) and \left(10, 5\right)

e

\left(10, 7\right) and \left(10, 2\right)

f

\left(10, - 2 \right) and \left( - 10 , - 2 \right)

g

\left( - 10 , 7\right) and \left( - 10 , 12\right)

h

\left( - 10 , 7\right) and \left(10, 7\right)

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Outcomes

MA5.1-6NA

determines the midpoint, gradient and length of an interval, and graphs linear relationships

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