Question

It cost $3$ to bowl a game and for shoe rental. How do you write an expression for the cost of g games?

Answer 1

Hint: Given a word problem. We have to determine the expression 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. First assume the variables which refer to a particular charge of the game.
So, let $g$ be the number of games and let $C$ be the total cost of games.
Now, in the next step we will find the slope which is equal to the amount for each additional game.
$ \Rightarrow m = 3$
Then, we will find the $y$-intercept which represents the fixed charges of the game that is cost of shoe rental.
$ \Rightarrow b = 2$
Now, we will substitute the values into the general equation of the linear equation.
$C = 3g + 2$

Final answer: Hence, the expression to represent the situation is $C = 3g + 2$.

Additional Information: In the linear equation, the slope is defined as the change in the value of one variable as the value of the second variable changes. It is used to define the variable cost of the situation. So, on the slope, we will define the cost which depends on the cost that is changing each hour. The y-intercept in the equation shows the fixed cost which does not change in the entire situation such as here the shoe rental is fixed whether one game or more than one game is played.

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.