Question

1. the height and weight of several adults were recorded:

it was discovered that this can be modeled by the equation ( y = 46.6x - 119 ) where ( x ) is height in feet and ( y ) is weight in pounds.

a) what does the slope of the line represent?

b) what does the y - intercept of this function represent?

c) using this model, what would be the weight of someone who is 4.85 ft tall? round your answer to the nearest tenth.

d) according to the model, what would be the weight of someone who is 6 ft tall? round your answer to the nearest tenth.

e) what height corresponds to a weight of 130 pounds? round your answer to the nearest hundredth.

Explanation:

Step1: Analyze the slope in the linear equation

The equation is in the form \(y = mx + b\) (slope - intercept form), where \(m\) is the slope. Here \(m = 46.6\). In the context of height (\(x\), in feet) and weight (\(y\), in pounds), the slope represents the change in \(y\) (weight) per unit change in \(x\) (height). So, for every 1 - foot increase in height, the weight increases by 46.6 pounds.

Step2: Analyze the y - intercept

In the equation \(y=46.6x - 119\), the \(y\) - intercept (\(b=- 119\)) occurs when \(x = 0\). But a height of \(x = 0\) feet is not physically meaningful in the context of adult height. Mathematically, it is the value of \(y\) (weight) when \(x\) (height) is 0, but in a real - world sense, it may not have a practical interpretation for the given data set (since adults have non - zero height).

Step3: Calculate the weight for \(x = 4.85\)

Substitute \(x = 4.85\) into the equation \(y=46.6x - 119\).

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Step4: Calculate the weight for \(x = 6\)

Substitute \(x = 6\) into the equation \(y = 46.6x-119\).

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Step5: Calculate the height for \(y = 130\)

Start with the equation \(y = 46.6x-119\) and solve for \(x\) when \(y = 130\).

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Answer:

a) For every 1 - foot increase in height, the weight increases by 46.6 pounds.
b) Mathematically, it is the weight when height is 0 (not physically meaningful for adult height in this context).
c) \(107.0\) pounds
d) \(160.6\) pounds
e) \(5.34\) feet