## TheJP 9 months ago Peter played his favorite video game for 10 hours last week. Today Peter's parents restricted him to 5 hours each week for the next 8 weeks. Create the function, f(x), that models Peter's total video game time and explain what each number in the situation represents graphically, using complete sentences.

1. TheJP

@myininaya

2. TheJP

3. TheJP

@theEric

4. theEric

Hi! I can help intermittently! If there's something I say that you don't understand, just let me know. Do you know what the independent variable will be?

5. TheJP

the 8 weeks?

6. theEric

Yep! Well, it mentions last week, too. So we should probably consider all 9 weeks. The independent variable, then, will be "weeks." Since we're writing your function as $$f(x)$$ because the problem says so, we will say that $$x$$ stands for the week number. How does that sound?

7. TheJP

Fantastic

8. theEric

Okay! So, we'll say that "today" is week 0. I changed my mind about including last week. I mean, I don't think that's what the problem is going for. So, at $$x=0$$, meaning zero weeks have passed, how many hours total have been played.

9. TheJP

if we have 0 weeks. then 0 hours?

10. theEric

Nope! Good guess, but Peter has some hours under his belt already.

11. TheJP

so 10 from last week?

12. theEric

Right! So, at $$x=0$$, we see that $$f(0)=10$$. Do you know the name for the value of the function when $$x=0$$? Starts with an 'i.'

13. TheJP

inverse?

14. theEric

Close! Not in meaning, but the spelling is close. interc---

15. TheJP

intercept?

16. theEric

You're right! :) So, if you have $$f(x)=mx+b$$ for a line, where is the intercept? (Hint, set $$x=0$$)

17. TheJP

m(0)+b =b

18. theEric

Right! The intercept is $$10\ \rm hours$$ and $$b$$ in the equation. So, when we finish, make sure you point out that the number "10" indicates the total hours played at the start of today, the "intercept." "Intercept will probably be a key word.

19. TheJP

Okay

20. TheJP

@david111

21. TheJP

??

22. TheJP

@theEric

23. theEric

5 hours per week, what does that tell you?

24. TheJP

x?

25. TheJP

i really have no idea

26. theEric

every one week, you gain five hours. If you have some scratch paper, it might help you see the picture by plotting this! Remember, start at $$f(0)=10$$ !