Savannah decides to research the relationship between the length in inches and the
weight of a certain species of catfish. She measures the length and weight of a number
of specimens she catches, then throws back into the water. After plotting all her data,
she draws a line of best fit. Based on the line of best fit, what would you predict to be
the length of a catfish that weighed 36 pounds?

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joaobezerra joaobezerra · Answer 1 · 2022-05-13T11:08:57+02:00

Using the line of best fit, it is found that the predicted length of a catfish that weighed 36 pounds is of 36 inches.

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, the line passes through points (20,4) and (29,22), hence the slope is given by:

m = (22 - 4)/(29 - 20) = 2.

Then:

y = 2x + b.

Point (20,4) is replaced in the equation and used to find b, hence:

4 = 2(20) + b

b = -36

Then the equation is given by:

y = 2x - 36.

When the weight is of 36 pounds, x = 36, hence the prediction is of:

y = 2(36) - 36 = 36 inches.

More can be learned about linear functions at https://brainly.com/question/24808124

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