Question

Tim's weight was 320 pounds in 2010 and is 180 pounds in 2020. Write a linear model to show Tim's weight since 2010.

Answer 1

Explanation

We are required to determine the linear model to show Tim's weight since 2010.

This is achieved thus:

Let x be the number of years from 2010.

Let y be Tim's weight.

Therefore, we have:

`\begin{gathered} (0,320) \\ (10,180) \\ \\ \text{ We know that the equation of a line given two points is:} \\ (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \end{gathered}`
`\begin{gathered} (y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ where \\ (0,320)\to(x_1,y_1) \\ (10,180)\to(x_2,y_2) \\ \\ \therefore(y-320)/(x-0)=(180-320)/(10-0) \\ (y-320)/(x)=(-140)/(10) \\ \text{ Cross multiply } \\ 10(y-320)=-140x \\ (10(y-320))/(10)=(-140x)/(10) \\ y-320=-14x \\ y=-14x+320 \end{gathered}`

Hence, the model is:

`y=-14x+320`