for what values of m is the line y=mx+2 at a distance 4 from (1,3)

Question

opcode · Answer

@Whatever1,
Welcome to OpenStudy. I hope you enjoy your stay here.
If you have any questions about the site ask the ambassadors. 
They have a purple Ⓐ by there name :)
Or you could always shoot me a PM.

@ParthKohli will now answer your question ^_^.

parthkohli · Answer

Okay, I thought OP would do it, but I will.

First, we have four points that are at distance 4 from $(1,3)$:$$(1,7) \ (1,-1) \ (5,3) \ (-3,3)$$There is another point but we'd look at it later.

parthkohli · Answer

Now, you just have to figure out the slopes where $y = mx + 2$ passes through these points. Can you do that?

parthkohli · Answer

There are actually many more points. There are infinite such points in fact. O_O

parthkohli · Answer

@Opcode shall help you with the rest. :-)