Question

part a
height the height of a woman can be predicted by the equation ( h = 81.2+3.34r ), where ( h ) is her height in centimeters and ( r ) is the length of her radius bone in centimeters.
a. what are the ( r ) - and ( h ) - intercepts of the equation? do they make sense in the situation? explain.
( h ) - int: ( - 81.2 )
( r ) - int: ( - 24.3 )
no, we would expect a woman 81.2 - cm tall to have a radius bone of a positive or negative length, and the length of the radius bone can be any real number
part b
b. graph the equation on a separate sheet of paper by using the intercepts.

Explanation:

Step1: Find the \(h\)-intercept

The \(h\)-intercept occurs when \(r = 0\).
Substitute \(r=0\) into the equation \(h = 81.2+3.34r\).

$$h=81.2 + 3.34\times0=81.2$$

Step2: Find the \(r\)-intercept

The \(r\)-intercept occurs when \(h = 0\).
Set \(h = 0\) in the equation \(0=81.2+3.34r\).
Solve for \(r\):

$$3.34r=- 81.2$$

$$r=\frac{-81.2}{3.34}\approx - 24.3$$

Step3: Analyze the intercepts in the context

The \(h\)-intercept (\(r = 0,h = 81.2\)): A woman with a radius - bone length of \(0\) cm (which is not physically possible as a bone length cannot be \(0\) in a living woman) is predicted to be \(81.2\) cm tall. This is a mathematical result but not practical in a real - world biological sense.
The \(r\)-intercept (\(h = 0,r\approx - 24.3\)): A height of \(0\) cm (a non - existent woman) would correspond to a negative radius - bone length. Since length (\(r\), radius - bone length) cannot be negative in a real - world biological context, this intercept does not make sense in the situation.

Answer:

• \(h\)-intercept: \((0,81.2)\)
• \(r\)-intercept: \((-24.3,0)\)
• The \(h\)-intercept does not make sense because a radius - bone length of \(0\) is not biologically valid for a living woman. The \(r\)-intercept does not make sense because the length of a bone (\(r\)) cannot be negative.