## eroshea 2 years ago find the point where the normal line to y = x + root x at (4,6) crosses the y-axis.

1. phi

did you find the equation for the slope of the curve?

2. eroshea

wait.. i'll solve for the slope

3. satellite73

take the derivative replace \(x\) by \(4\) that gives you the slope take the negative reciprocal, that give you the slope of the normal line use the point slope formula with the point \((4,6)\) to find the equation of the normal line \(y=mx+b\) then \(b\) is where it crosses the y axis

4. eroshea

the value of b is the answer then?

5. satellite73

yes, that is the y intecept

6. eroshea

ok.. thanks.. i'll try solving for it

7. phi

Here is a plot of the scenario

8. eroshea

thanks! what i got was 31/5 .. is this correct?

9. phi

how ?

10. eroshea

i follow the steps satelite gave

11. phi

I think you wandered off the path...

12. eroshea

why??

13. phi

see the plot I posted up above

14. eroshea

where is the normal line there?

15. phi

the red line

16. eroshea

so what do you think is wrong with my answer? is the steps given by satelite somehow have mistakes? i just followed it

17. phi

what did you get for the slope ?

18. phi

first, what did you get for the derivative?

19. eroshea

owh wait.. i got a mistake

20. eroshea

b = 46/5 .. i believe that is the correct answer now?

21. phi

yes, 9.2 which matches the plot

22. eroshea

9.3 :)) thanks so much! help me again.. i'll post a question :)

23. phi

9.3 ?

24. eroshea

yes.. divide 46 by 5 right ? then it will be 9... remainder is 15.. that will be 3.. so 9.3?

25. phi

5*9= 45

26. eroshea

lol.. i got a mistake again. sorry.. yes.. 9.2