Question

The scatter plot and line of best fit below show the length of 12 people's femur (thelong leg bone in the thigh) and their height in centimeters. Based on the line of besfit, what would be the predicted height for someone with a femur length of 72 cm?Answer: ____ cm.

Answer 1

The predicted height is approximately 230 cm.

Let's find the predicted height for someone with a femur length of 72 cm using the line of best fit:

1. Find the Slope (m):

   • Using the given points (63, 209) and (72, 230), the slope is calculated as:

   m = (230 - 209) / (72 - 63) = 2.333

2. Write the Equation of the Line (Point-Slope Form):

   • Using the point (63, 209), the equation is:

   y - 209 = 2.333(x - 63)

3. Substitute x = 72 into the Equation:

   • Substituting x = 72 gives:

   y - 209 = 2.333(72 - 63)

   y - 209 = 2.333(9)

   y - 209 = 20.997

4. Add 209 to Both Sides:

   • Adding 209 to both sides of the equation gives:

   y = 20.997 + 209

   y = 229.997

5. Round to the Nearest Whole Number:

   • Rounding to the nearest whole number, the predicted height is approximately 230 cm.

Therefore, the predicted height for someone with a femur length of 72 cm is approximately 230 cm.

Answer 2

230

Step-by-step explanation:

First, we find the equation fo the line point-slope form.

The slope of the line is

`m=(209-202)/(63-60)=(7)/(3)`

With the slope of the line in hand, we now write the point-slope form of the equation using the point (63, 209)

`y-209=(7)/(3)(x-63)`

With the equation of the line in hand, we now use it to find the value of y at x = 72.

Putting in x = 72 in the above equation gives

`y-209=(7)/(3)(72-63)`
`y-209=(7)/(3)\cdot9`
`y-209=21`

adding 209 to both sides gives

`y=230`

which is our answer!

Hence, the predicted height for someone with a femur length of 72 cm is 230 cm.