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 the

Vectors and spaces
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asked 2021-05-01
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.

Answers (2)

2021-05-02

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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Best answer
2021-09-14

Answer is given below (on video)

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