Question

The average height of a 2 year old boy is 38 inches.an 8 year old averages 56 inches. Use this information to write a linear equation that models

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ANSWERED
asked 2021-09-05
The average height of a 2 year old boy is 38 inches. an 8 year old averages 56 inches. Use this information to write a linear equation that models the height (in inches), y, in terms of the age (in years), x. Use the linear equation to predict the average height of a 5 year-old boy.

Expert Answers (1)

2021-09-06
Represent the given data as points: (x1,y1)=\(\displaystyle{\left({2},{38}\right)}→{2}\) year old boy is 38 inches year old boy is 38 inches
(x2,y2)=\(\displaystyle{\left({8},{56}\right)}→{8}\) year old boy is 56 inches year old boy is 56 inches
Find the slope \(\displaystyle{m}=\frac{{{y}{2}-{y}{1}}}{{{x}{2}-{x}{1}}}=\frac{{{56}-{38}}}{{{8}-{2}}}=\frac{{18}}{{6}}={3}\)
Use the slope-intercept form of a line: y=mx+b
Substitute any point, say (2,38) and m=3 to find bb:
38=3(2)+b
38=6+b
32=b
So, the linear equation is: y=3x+32
To predict the average height of a 5 year-old boy, substitute x=5:
y=3(5)+32
y=15+32
\(\displaystyle{y}={47}→{47}\) inches
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