Question

How do you create a linear model in a word problem?

Answer 1

Hint: Given a word problem. We have to determine the method by which a linear model is created for a word problem. First, we will assume the variables x and y. Now, we will determine the slope of the equation and then determine the y-intercept of the linear model.

Formula used:
The general equation of linear model is given by:
$y = mx + b$

Complete step-by-step answer:
We are given the word problem. For example, the fixed rate of parking a car is $\$ 3.00$ for $2$ hours or less than it and for each additional hour, the charges are $\$ 0.70$ per hour. Determine the linear model which gives the total charge of parking.
First, assume the variables which refer to a particular charge of parking.
So, let $x$ be the number of additional hours of parking and let $y$ be the total amount of parking.
Now, in the next step we will find the slope which is equal to the amount for each additional hour.
$ \Rightarrow m = 0.70$
Then, we will find the $y$-intercept which represents the fixed charges of parking.
 $ \Rightarrow b = 3$
Now, we will substitute the values into the general equation of the linear equation.
$y = 0.70x + 3$

Final answer: Hence, the linear model is created by first assuming the variables and then determining the value of slope and $y$-intercept. Then, substitute them into the general equation of the linear equation.

Note:
In such types of questions the students mainly don't get an approach on how to solve it. In such types of questions students mainly forget to substitute the value of the slope and $y$-intercept.