Y intercepts to a tangent line

Question

Find the y intercepts of a tanget line to the curve y=(x-1)/(x+1) that the line is parallel to x-2y=4

Answer 1

x-2y=4

rewrite in slope intercept

slope=1/2

where is the slope of the curve equal to 1/2

dy/dx=((x+1)-(x-1))/(x+1)²=2/(x+1)²

1/2=2/(x+1)² (x≠-1)

Solve

(x+1)²/2=2(x+1)²/(x+1)²

2(x+1)²/2=2(2)

(x+1)²=4

x+1=±2

x=1 x=-3

Find y values from original curve at x=1 and x=-3

y=(1-1)/(1+1)=0

y=(-3-1)/(-3+1)=-4/-2=2

so the points where the tangent lines are parallel to the line are (1,0) and (-3,2)

Find y-intercept of tangent line

y=mx+b

y=(1/2)x+b

0=(1/2)(1)+b

-1/2=b

y intercept is (0,-1/2)

y=(1/2)x+b

2=(1/2)(-3)+b

7/2=b

y intercept is (0,7/2)