Answer:
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
Step-by-step explanation:
* Lets explain how to solve the problem
- The slope of the line whose end points are (x1 , y1) and (x2 , y2) is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- 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
∴ [tex]m=\frac{50-43}{14-12}=\frac{7}{2}[/tex]
∵ 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
