Using the Slope of a Line to Estimate Fish Weight

Fish Grow All of Their Lives

• They first start out as an embryo in an egg.

• Then they hatch out as a larvae.

• Then they develop into a juvenile.

• Then they become an adult.

Fish Growth

• As fish grow, their weight increases proportionally to their length.

Determining the Length-Weight Relationship

• First, you need to measure the length and weight for several fish.

Number Length Weight1 11 92 5 53 15 134 12 115 18 176 17 187 9 128 7 99 2 4

10 6 411 13 1412 8 813 20 1914 16 1615 10 1116 4 317 19 2118 3 319 1 120 14 16

Length

Graphing the Data

• The next step is to graph the data and draw a line of best fit.

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Length (cm)

Wei

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The Line EquationY = mX + b

• The ‘slope’ of the line (m) is the relationship between length and weight.

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Increase in Weight

Increase in Length

Slope

Estimating Weight From Length• Once you know the length-weight

relationship for a species, you can estimate the weight based only on the length!

Weight = 0.9909(Length) + 0.2814

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Y=mX + b

Estimating Weight From a Line Equation

• Our Line Equation is: Weight = 0.9909(Length) + 0.2814

• 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

• Some fish are long and skinny and some are short and fat.

Comparing Fish Species

• The length-weight relationship for long skinny fish is different than for short fat fish.

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Length (cm)

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) Long and Skinny Fish

Short and Fat Fish