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