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:} \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}$$\begin{gathered} \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ where \\ (0,320)\to(x_1,y_1) \\ (10,180)\to(x_2,y_2) \\ \\ \therefore\frac{y-320}{x-0}=\frac{180-320}{10-0} \\ \frac{y-320}{x}=\frac{-140}{10} \\ \text{ Cross multiply } \\ 10(y-320)=-140x \\ \frac{10(y-320)}{10}=\frac{-140x}{10} \\ y-320=-14x \\ y=-14x+320 \end{gathered}$

Hence, the model is:

$y=-14x+320$