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?

Explanation:

a)

The equation of a line is \(y = mx + b\), where \(m\) is the slope. In the context of \(y = 46.6x-119\) (with \(x\) as height in feet and \(y\) as weight in pounds), the slope \(m = 46.6\).
The slope represents the rate of change of \(y\) with respect to \(x\). So, for every 1 - foot increase in height (\(x\)), the weight (\(y\)) increases by 46.6 pounds.

b)

The \(y\) - intercept of the line \(y=mx + b\) is \(b\). In the equation \(y = 46.6x-119\), the \(y\) - intercept \(b=- 119\).
When \(x = 0\) (height is 0 feet, which is not a realistic physical height for an adult in this context, but from a mathematical perspective of the linear model), the \(y\) - intercept represents the predicted weight. However, since height cannot be 0 for an adult, it may not have a practical physical meaning in the real - world scenario of adult height - weight relationship, but it is a part of the linear mathematical model.

Answer:

a)

The slope of the line represents the increase in weight (in pounds) for each 1 - foot increase in height.

b)

The \(y\) - intercept represents the predicted weight (in pounds) when the height (\(x\)) is 0 feet (a value that is not physically relevant for an adult's height - weight relationship but is a component of the linear mathematical model).