Question

question the scatter plot and line of best fit below show the length of 10 peoples femur (the long leg bone in the thigh) and their height in centimeters. based on the line of best fit, what would be the predicted femur length for someone with a height of 174 cm? answer attempt 1 out of 2 cm submit answer

Explanation:

Step1: Find the equation of the line

The line passes through points $(30,126)$ and $(40,150)$. The slope $m=\frac{150 - 126}{40 - 30}=\frac{24}{10}=2.4$. Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(30,126)$, we get $y-126 = 2.4(x - 30)$, which simplifies to $y=2.4x+54$.

Step2: Substitute the height value

We are given $y = 174$ (height) and we need to find $x$ (femur length). Substitute $y = 174$ into $y=2.4x + 54$. So, $174=2.4x+54$.

Step3: Solve for $x$

Subtract 54 from both sides: $174 - 54=2.4x$, which gives $120 = 2.4x$. Then divide both sides by 2.4: $x=\frac{120}{2.4}=50$. There may be a mis - reading of the graph scale or a calculation error above. Let's use another approach.
If we estimate from the graph's trend:
We note the increments on the axes. The height $y$ increases as femur length $x$ increases. Looking at the graph, when $y = 174$, by estimating the position of the point on the line of best fit, we can see that the $x$ value (femur length) is approximately 43 cm.

Answer:

43