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
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.

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

2021-09-14

Answer is given below (on video)