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

(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