write the equation for the tangent line in slope intercept form

2x^2+3xy+3y^2=17;(2,1)

Question

write the equation for the tangent line in slope intercept form

2x^2+3xy+3y^2=17;(2,1)

anonymous · Answer

anything will help please!

anonymous · Answer

did you get 
$$y'$$?

anonymous · Answer

i got it wrong lol thats what happened..ive done it twice..i only get one more chance

anonymous · Answer

ok lets see 
$$2x^2+3xy+3y^2=17$$
$$4x+3y+3xy'+6yy'=0$$ right?

anonymous · Answer

i got that yes

anonymous · Answer

$$4\times 2+3\times 1+3\times 2y'+6\times 1\times y'=0$$
$$8+3+6y'+6y'=0$$
$$11+12y'=0$$
$$12y'=-11$$
$$y=-\frac{11}{12}$$
check my algebra since you only have one more chance

anonymous · Answer

well i need the actual equation..so it would be y=-11/12x with the y intercept

anonymous · Answer

assuming i did not make an arithmetic mistake, which you really should check, you have the slope as 
$$-\frac{11}{12}$$and then point - slope formula give 
$$y-1=-\frac{11}{12}(x-2)$$

anonymous · Answer

ill check it...but is it going to be -11/12x-1?

anonymous · Answer

oh no

anonymous · Answer

it will be what i wrote, and if you solve for y you should get 
$$y=-\frac{11}{12}x+\frac{17}{6}$$

anonymous · Answer

ok ill check the math and let you know

anonymous · Answer

it was right!!! =)

anonymous · Answer

thanks

anonymous · Answer

yw
don't forget point slope formula!