Question

breas actual weight is 72 pounds, and her actual height is 55 inches tall. what is the difference, in inches, between breas actual height and her height as predicted by the function? round your answer to the nearest hundredth.

Explanation:

Step1: Find two points on the line

Let's take two points \((x_1,y_1)=(0,25)\) and \((x_2,y_2)=(10,30)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
\(m=\frac{30 - 25}{10-0}=\frac{5}{10}=0.5\)

Step3: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\), with \((x_1,y_1)=(0,25)\) and \(m = 0.5\)
The equation is \(y=0.5x + 25\)

Step4: Predict the height when \(x = 72\)

Substitute \(x = 72\) into the equation \(y=0.5x+25\)
\(y=0.5\times72 + 25=36+25=61\)

Step5: Calculate the difference

The actual height is \(y_{actual}=55\)
The difference \(d=\vert y_{predicted}-y_{actual}\vert=\vert61 - 55\vert = 6\)

Answer:

\(6.00\)