# Linear System Flyer

## Situation

The height of 2 fraternal twins is measured for 30 months after birth by their mother so they can see the rate at which their child is growing. By doing this they can estimate when their clothes will get small on them so the mother can buy clothes that are the right size in advance. One child's name is Aryan, and the other's name is Robin, both are boys.

Aryan is 46 cm at birth and Robin is 33.5 cm. Aryan grows at a constant 2 cm per month, and Robin grows at a constant 2.5 cm per month. Both had a regular birth after 9 months of pregnancy. Their mother stopped collecting data for each when they reached 110 cm because her husband promised to shop for their clothes when they reached 110 cm in height.

## Height Equations

The equation used to find Aryan's height is

y=2x+46

Y represents Aryan's height, and x represents Aryan's age in months.

The equation used to find Robin's height is

y=2.5x+33.5

Y represents Robin's height, and x represents Robin's age in months.

## Solution

The solution for this set of data may be obtained by the graph, a table or substitution, in this case the method used was the graph, and a table. I know my solution is correct because on my table of values (paper version) the data agreed with the Desmos graphing calculator's answer for the point of intersect.

## Summary

The boys will be of equal height at 25 months because they grow and different, but constant speeds, and before 25 months of age Aryan is taller, and after 25 months of age Robin will be taller. At the These growth patterns can be represented by a linear equation due to the constant growth speed. The equation used in this flyer is slope, y-intercept form or y=mx+b. In this equation y represents the y value which in this case is total height, m represents the slope which is the growth rate in this case, and b represents the y-intercept which is the initial height of the babies in this case. The solution of this equation can be obtained by examining the graph, and the point of intercept represents the age at which they have equal height. the solution for this set of data is (25, 9) at this point both are 25 months old and 96 cm tall.