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# Using the Slope of a Line to Estimate Fish Weight

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```Using the Slope of a Line to
Estimate Fish Weight
Fish Grow All of Their Lives
вЂў They first start out as an
embryo in an egg.
вЂў Then they hatch out as a
larvae.
вЂў Then they develop into a
juvenile.
вЂў Then they become an
Fish Growth
вЂў As fish grow, their weight increases
proportionally to their length.
Determining the Length-Weight
Relationship
вЂў First, you need to
measure the length
and weight for
several fish.
Length
N um ber
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
L e n g th
11
5
15
12
18
17
9
7
2
6
13
8
20
16
10
4
19
3
1
14
W e ig h t
9
5
13
11
17
18
12
9
4
4
14
8
19
16
11
3
21
3
1
16
Graphing the Data
вЂў The next step is to graph the data and
draw a line of best fit.
25
Weight (g)
20
15
10
5
0
0
5
10
Length (cm)
15
20
The Line Equation
Y = mX + b
вЂў The вЂ�slopeвЂ™ of the line (m) is the
relationship between length and weight.
25
20
Weight (g)
Slope
15
Increase in Weight
10
Increase in Length
5
0
0
5
10
Length (cm)
15
20
Estimating Weight From Length
вЂў Once you know the length-weight
relationship for a species, you can
estimate the weight based only on the
length!
25
Y=mX + b
Weight (g)
20
Weight = 0.9909(Length) + 0.2814
15
10
5
0
0
5
10
Length (cm)
15
20
Estimating Weight From a Line Equation
вЂў Our Line Equation is: Weight = 0.9909(Length) + 0.2814
вЂў How much would you expect a 12 cm fish to weigh?
Weight = 0.9909(12) + 0.2814
Weight = 11.8909 + 0.2814
Weight = 12.1722
Comparing Fish Species
вЂў Some fish are long and skinny and
some are short and fat.
Comparing Fish Species
вЂў The length-weight relationship for long
skinny fish is different than for short fat
fish.
25
Short and Fat Fish
Weight (g)
20
Long and Skinny Fish
15
10
5
0
0
5
10
Length (cm)
15
20
```
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