Question

Joe took $12 to the arcade. Each game cost $.50 to play. This situation can be modeled with the equation y + -.50 x+ 12. This represents the relationship between money Joe has remaining, y, and the number of games he plays, x. Use the function to determine the y-intercept.

State the meaning of the y-intercept in the terms of this problem

Answer 1

y-intercept is 12 and y-intercept shows the fixed cost of arcade, i.e., $12.

Explanation:

Note : The given equation is not correct.

It is given that Joe took $12 to the arcade and each game cost $0.50 to play.

This situation can be modeled with the equation

`y=0.50x+12`

where, y is total cost of playing x games.

We need to find y-intercept.

Substitute x=0 in the above equation to find the y-intercept of the equation.

`y=0.50(0)+12`

`y=0+12`

`y=12`

So, the y-intercept is 12.

Here y-intercept represents the total cost if the number of games is zero.

It means y-intercept shows the fixed cost of arcade, i.e., 12.

Answer 2

Answer: Joe has initial amount of $12 ( when he played no game).

Explanation:

Given: Joe took $12 to the arcade. Each game cost $.50 to play.

This situation can be modeled with the equation
`y =-0.50 x+ 12.`

Here,

Money Joe has remaining is repreesnted by 'y', and the number of games he plays is represented by 'x'.

Since y-intercept gives the initial value of the function when x=0.

To find y-intercept , we out x=0 in funtion , we get

`y=-0.50(0)+12=12`

So , y-intercept of this function is at y=12.

Meaning of the y-intercept in the terms of this problem :

Joe has initial amount of $12 ( when he played no game).