Michael797 Group Title (Graph Attached) The graph below shows the revenue earned by a company in its first four quarters of operation. A line of best fit has been drawn on the graph. Based on the linear model, how much revenue, in thousands of dollars, should the company earn in its 7th quarter of operation? Type your answer in the box below. 2 years ago 2 years ago

1. Michael797 Group Title

2. Akshay_Budhkar Group Title

Step 1: Find the equation of that line, by finding the slope using the two points giving, Step2:substitute x=7 and find the value of y. Can you find the equation of that line?

3. Michael797 Group Title

i'm sorry but how would I find the equation from this?

4. Akshay_Budhkar Group Title

You can see the two points on the line (1,10) and (3,30) So the slope is 10, now using the slope-point form the equation of that line is (y-10)/(x-1)=10

5. Akshay_Budhkar Group Title

Slope=m= (y2-y1)/(x2-x1)

6. Michael797 Group Title

Yeah so then that would go to...30 - 10 / 3 - 1 or 20 / 2. That simplifies to 10 / 1 or just 10

7. Akshay_Budhkar Group Title

Exactly, Now to find the equation, take any 1 point, use y-y1/x-x1=m=10 Then solve this to get the equation of that line and then just substitute x=7 to get the value of y :)

8. Akshay_Budhkar Group Title

i used (1,10) above^

9. Michael797 Group Title

m = 10. x = 7 But what does b equal, cause if i'm gonna put it in an equation how would I get the "b" in y=mx+b?

10. Akshay_Budhkar Group Title

nope, not in that manner,

11. Akshay_Budhkar Group Title

see to find the equation take any point (x,y) and a point you know (lets take (1,10) ) so now we know the slope is 10.. but the slope is also${(y2-y1)\over(x2-x1)}={(y-10)\over(x-1)}=m=10$

12. Akshay_Budhkar Group Title

taking x2,y2 as x,y and x1,y1 as 1,10

13. Michael797 Group Title

My brain is not working but thank you for the patience, it's 2 am lol. I'm just trying to finish this last question. But Ok yes that all equals m=10 and now that we know the slope, and we know the Y intercept is 10.

14. Michael797 Group Title

Because the point we chose is (1,10)

15. Akshay_Budhkar Group Title

nope, see the equation above^ just solve that, so what do we get$y-10=10(x-1) \therefore y-10=10x-10 \therefore y=10x$

16. Akshay_Budhkar Group Title

so thats the equation of your line!

17. Akshay_Budhkar Group Title

the intercept is zero, u need to slove the equation above

18. Akshay_Budhkar Group Title

and its 2am here as well i got work in the morning :P

19. Michael797 Group Title

Would the final answer be 70,000 it looks as if it would be right

20. Michael797 Group Title

After estimating the graph it looks almost exactly that once it reaches 7, it would be at 70,000

21. Michael797 Group Title

Oh how could I not realize...the 1 is on 10,000, the 3 is on 30,000, the 4 is on 40,000 jeez I made this alot harder than it it LOL

22. Akshay_Budhkar Group Title

yea thats your answer, see you dont always need the intercept to write the equation, if u got the slope and a point we get the equation as shown above^ And yes it was so simple, i could have told you the shortcut , but i went through the steps :P

23. Michael797 Group Title

Yeah and thanks for showing me!

24. Akshay_Budhkar Group Title

no problem :)