Question

Find equations of the tangent lines to the curve
y = (x − 1)/(x + 1)
that are parallel to the line
x − 2y = 3.

Answer 1

find the slope of x-2y=3

find y' given y=(x-1)/(x+1)

we want the slope of the linear equation to have the same slope as a tangent line of y=(x-1)/(x+1)
so do the following
set slope of linear line=y' and solve for x

Answer 2

im confused
the answer I need to find has 2 equations; each with a different y-intercept

Answer 3

so what did you get for the slope of the linear equation above?

Answer 4

1/2

Answer 5

ok what did you get when finding y' given y=(x-1)/(x+1)?

Answer 6

\[2/(x+1)^2\]

Answer 7

[(x+1)-(x-1)]/(x+1)^2
yes i agree
gj
now set this =1/2 and solve for x

Answer 8

2/(x+1)^2=1/2

Answer 9

2/4=1/2 right?

Answer 10

so we want (x+1)^2=4?

Answer 11

so
x+1=2
or
x+1=-2

Answer 12

=> we have the curve has the same slope as x-2y=3 at x=1 or x=-3

Answer 13

i will find one equation for you
you can do the other
we have two equations one for x=1 and one for x=-3
------------
IF x=1, then y=(x-1)/(x+1)=(1-1)/(1+1)=0
so we know a point on the tangent line (1,0)
remember slope is 1/2
so we have
the tangent equation at x=1 has form y=mx+b
where m=1/2 and we can find b the y-intercept since we know a point (x=1,y=0)
pluggin' this in we get
0=1*1/2+b
-1/2=b
so the equation at x=1 with slope 1/2 is
y=x/2-1/2

Answer 14

so you can do it for x=-3

Answer 15

I'm getting more confused as you go on haha

Answer 16

are you confused with the calculus part or the algebra part?

Answer 17

it has to be the algebra part since we already done the cal part

Answer 18

if we know a point on a line and the slope, then we can find the equation of the line right?
we have the slope m=1/2
and we have the point (1,0)
just plug into y=mx+b and solve for b
then we have it

Answer 19

well we have a point on the line*