Question

How do you find a linear model?

Answer 1

Hint: In this question, we need to explain the steps of finding a linear model. Firstly, we must know the meaning of linear models. So a linear model is an equation that describes a relationship between two quantities that shows a constant rate of change. To write a linear model we need to know both the rate of change and the initial value. Once we have written a linear model, we can use it to solve all types of problems.

Complete step by step solution:
Let us find the solution for the given question.
We are asked to find a linear model. i.e. we need to tell the steps of determining a linear model.
Firstly, let us give the definition of a linear model. So that it will be easier to understand.
A linear model is an equation that describes a relationship between two quantities that show a constant rate of change.
Linear models describe a continuous response variable as a function of one or more predictor variables.
For experimental data it may be appropriate to use linear regression. On the other hand, for precise data you do not need linear regression.
If you have a number of experimentally generated data points that are subject to inaccuracies, then you can use something like linear regression to generate a linear model that fits the data reasonably well. Many modern calculators have a linear regression capability.
On the other hand, if you are given precise data, you should be able to generate a model that fits the data exactly.
We represent linear relationships graphically with straight lines. A linear model is usually described by two parameters : the slope, also called as the growth factor or rate of change, and y-intercept, also called as the initial value.
For example, if you have given the slope $m$ and the y-intercept $c$, the linear model can be written as a linear function given by, $y = mx + c$, which is a slope intercept form.
If we have given two points, $({x_1},{y_1})$ and $({x_2},{y_2})$ which are supposed to lie on a line, the equation of the line in point slope form is,
$y - {y_1} = m(x - {x_1})$, where $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$.
And we have $c = {y_1} - m{x_1}$.

Note :
Students must remember that to write a linear model, we need to know both the rate of change and the initial value. Once we have written a linear model, we can use it to solve all types of problems.
We explain this, through an example.
A club has 200 members. The club plans to increase membership by 25 members every year.
Now we have to write an equation to represent the relationship between the number of members y, and the years from now x.
The initial value is 200 and the rate of change is 25.
Therefore, the linear model is given by $y = 25x + 200$.