1. Lines – Gradient – Worksheet B
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3. 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡= 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 ℎ𝑜𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡= 3 3 =1 3 3

4. 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡= 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 ℎ𝑜𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡= ?

5. × × × × × × × × × × × × × × × × 1 Finding Gradients D N P C I G J O B
The gradient of a line tells us
how steep it is.
We measure gradient by comparing
the vertical change with the horizontal change.
Finding Gradients
Gradient =
horizontal change
vertical change kk × D × N kk kk kk × P +3
= 3 +1
Gradient = +3
= 1
Gradient = −2
= −2 +1
Gradient = × C × I
We can also say,
“A line with gradient +2, goes up two for every one across”.
“A line with gradient -3, goes down three for every one across”. × G
Calculate the gradient of these lines from the grid. × J
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
A⬌B 2
B⬌C
C⬌D 6
E⬌F 3
F⬌G 9
G⬌H −8
D⬌I
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
I⬌J
E⬌K
K⬌L
K⬌M
C⬌N
H⬌O
D⬌P × O × B × H × A × F × L × K × E × M

6. × × × × × × × × × × × × × × × × 1 2 4 1 3 −2 −3 Finding Gradients D N
The gradient of a line tells us
how steep it is.
We measure gradient by comparing
the vertical change with the horizontal change.
Finding Gradients
Gradient =
horizontal change
vertical change kk × D × N kk kk kk × P +3
= 3 +1
Gradient = +3
= 1
Gradient = −2
= −2 +1
Gradient = × C × I
We can also say,
“A line with gradient +2, goes up two for every one across”.
“A line with gradient -3, goes down three for every one across”. × G
Calculate the gradient of these lines from the grid. × J
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
A⬌B 2
B⬌C 4
C⬌D 1
E⬌F
F⬌G 3
G⬌H − −2
D⬌I − −3
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
I⬌J − −1
E⬌K
1 2 , 0.5
K⬌L
1 3 , 0.33
K⬌M −
− 1 3 , −0.33
C⬌N − −5
H⬌O 2
D⬌P −
− 1 2 , −0.5 × O × B × H × A × F × L × K × E × M

7. × × × × × × × × × × × × × × × 2 2 4 3 −2 1 −3 −1 Finding Gradients D O
The gradient of a line tells us
how steep it is.
We measure gradient by comparing
the vertical change with the horizontal change.
Finding Gradients
Gradient =
horizontal change
vertical change kk × D × O kk kk kk × L +3
= 3 +1
Gradient = +3
= 1
Gradient = −2
= −2 +1
Gradient = × C × G × F
We can also say,
“A line with gradient +2, goes up two for every one across”.
“A line with gradient -3, goes down three for every one across”.
Calculate the gradient of these lines from the grid.
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
A⬌B 2
B⬌C 4
C⬌D 3
C⬌E − −2
E⬌F 1
D⬌G − −3
G⬌H − −1
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
B⬌I − −4
I⬌J
1 2 , 0.5
J⬌K
1 3 , 0.33
C⬌L −
J⬌M −
− 1 2
K⬌N −
− 1 4
F⬌O −
− 3 2 , −1.5 × H × B × E × N × A × K × J × I × M

8. × × × × × × × × × × × × × × × × 1 Finding Gradients D N P C I G J O B
The gradient of a line tells us
how steep it is.
We measure gradient by comparing
the vertical change with the horizontal change.
Finding Gradients
Gradient =
horizontal change
vertical change kk × D × N kk kk kk × P +3
= 3 +1
Gradient = +3
= 1
Gradient = −2
= −2 +1
Gradient = × C × I
We can also say,
“A line with gradient +2, goes up two for every one across”.
“A line with gradient -3, goes down three for every one across”. × G
Calculate the gradient of these lines from the grid. × J
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
A⬌B 2
B⬌C
C⬌D 6
E⬌F 3
F⬌G 9
G⬌H −8
D⬌I
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
I⬌J
E⬌K
K⬌L
K⬌M
C⬌N
H⬌O
D⬌P × O × B × H × A × F × L × K × E × M

10. × × × × × × × × × × × × × × × 2 Finding Gradients D O L C G F H B E N
The gradient of a line tells us
how steep it is.
We measure gradient by comparing
the vertical change with the horizontal change.
Finding Gradients
Gradient =
horizontal change
vertical change kk × D × O kk kk kk × L +3
= 3 +1
Gradient = +3
= 1
Gradient = −2
= −2 +1
Gradient = × C × G × F
We can also say,
“A line with gradient +2, goes up two for every one across”.
“A line with gradient -3, goes down three for every one across”.
Calculate the gradient of these lines from the grid.
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
A⬌B 4
B⬌C 2
C⬌D
C⬌E −8
E⬌F
D⬌G
G⬌H
𝑳𝒊𝒏𝒆
𝒗𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝒉𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕
B⬌I
I⬌J
J⬌K
C⬌L
J⬌M
K⬌N
F⬌O × H × B × E × N × A × K × J × I × M

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