Wierzycaz

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.

i1ziZ

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

Jeffrey Jordon