# Applications Using Linear Models

## Key Questions

• To find a linear function (model), we need two pieces of information:

$\left\{\begin{matrix}\text{Point: " (x_1y_1) \\ "[Slope](http://socratic.org/algebra/graphs-of-linear-equations-and-functions/slope): } m\end{matrix}\right.$

So, find them from the description of the problem, then use Point-Slope Form

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

to come up with the equation.

I hope that this was helpful.

• The major practical application for linear models is to model linear trends and rates in the real world.

For example, if you wanted to wanted to see how much money you were spending over time, you could find how much money you had spent at a given time for several points in time, and then make a model to see what rate you were spending at.

Also, in cricket matches, they use linear models to model the run rate of a given team. They do this by taking the number of runs a team has scored in a certain number of overs, and divide the two to come up with a runs per over rate.

However, keep in mind that these real-life linear models are usually always averages, or approximations . This is just due to life being so random, but we never actually stick to those rates we have. For example, if a cricket team's run rate was judged to be 10.23 runs per over, it doesn't mean that they scored exactly 10.23 runs every over, but rather that they scored that many on average.

Hope that helped :)

A general approach is to let the variable be whatever the question asks you to find......

#### Explanation:

A general approach is to let the variable be whatever the question asks you to find......

Find the number. Let the number be $x$

How many toys does Pete have? Let the number of toys be $x$

What is the price of the shirt? Let the price be $x$

If you are asked to find two numbers,
or the length and breadth of a rectangle
or the ages of a mother and her son
or the price of pears and peaches, then.....

Let the variable be the smaller number and then write an expression for the other value.

When each unknown has been defined with a variable, then write the equation.

e.g. The sum of two numbers is 15:
Let the smaller number be $x$ and the larger be $15 - x$

The sum of three consecutive numbers is $57$
Let the numbers be:$\text{ "x," " x+1," } x + 2$

Sometimes you will not be given a specific relationship between the numbers. In this case use two variables.

Let the numbers be $x \mathmr{and} y$