Question

At age 12 Patrick weighed 43 kg; at age 14 he weighed 50 kg. Patrick’s age and weight are related. A) find a linear equation relating Patrick’s weight to his age B) use your equation to find out Patrick’s age when he weighed 38kg

Answer 1

A) The equation relating Patrick’s weight to his age is y = 7/2 x + 1

B) The Patrick's age is 10.57 years when he weighed 38 kg

Explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) and (x2 , y2) is

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

- The form of the linear equation is y = mx + c, where m is the slope of

the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

* Lets solve the problem

- At age 12 Patrick weighed 43 kg

- At age 14 he weighed 50 kg

- Represent the age by x and the weight by y

∴ There are two points on the line which represents the relation

between the age and the weight of Patrick

∵ (12 , 43) and (14 , 50) belong to the equation relating Patrick’s

weight to his age

A)

- Lets find the equation

∵ (x1 , y1) is (12 , 43) and (x2 , y2) is (14 , 50)

∴ x1 = 12 , x2 = 14 and y1 = 43 and y2 = 50

∴
`m=(50-43)/(14-12)=(7)/(2)`

∵ y = mx + c

∴ y = 7/2 x + c

- To find c by substitute x and y in the equation by the coordinates

of one of the 2 points

∵ 43 = 7/2 (12) + c

∴ 43 = 42 + c

- Subtract 42 from both sides

∴ c = 1

∴ The equation is y = 7/2 x + 1

* The equation relating Patrick’s weight to his age is y = 7/2 x + 1

B)

∵ The weight of Patrick is 38 kg

- That means y = 38

∵ y = 7/2 x + 1

∴ 38 = 7/2 x + 1

- Subtract 1 from both sides

∴ 37 = 7/2 x

- Divide both sides by 7/2

∴ x = 37 ÷ 7/2 = 10.57

∴ The Patrick's age is 10.57 years when he weighed 38 kg