Find P on y = 1/x so slope thru P & (2, 1/2) is m = -1/10

[caseygaspar]

Okay so last question for the day... I have to find a point P on the curve y=1/x such that the slope of the line drawn through P and the point (2,1/2) is -1/10

Ok so I started off with using the point slope formula and I ended up with y= -1/10x +7/10 I got stuck here because I didn't see any relation...
I am sort of confused with this topic..... :roll:

 

[stapel]

I started off with using the point slope formula and I ended up with y= -1/10x +7/10....

In future, it might be helpful if you could please include what you've done...? It's hard to find errors in steps we can't see.

You have P on y = 1/x, so P = (x, 1/x). You are given that you have to have:

. . . . .\(\displaystyle m\, =\, \frac{\frac{1}{x}\, +\,\frac{1}{2}}{x\, -\, 2}\, =\, -\frac{1}{10}\)

Multiplying top and bottom of the middle "half" by 2x, you get:

. . . . .\(\displaystyle m\, =\, \frac{2\, +\, x}{2x(x\, -\, 2)}\, =\, -10\)

. . . . .\(\displaystyle (2\, +\, x)\, =\, -10\left(2x(x\, -\, 2)\right)\)

Solve the quadratic for the values of x.

Eliz.

Edited to correct slope-formula typo.