Find the point p on the graph y=1/5x such that the slop of the line through (1,1/5) and p is -1/7?

Question

I'm stuck on this. I used the definition of slope to find x but I keep getting 5/7 and that doesn't seem to be right.

Answer 1

The point (1,1/5) lies on the line y= 1/5x
Therefore the point p is (1,1/5).

The line passing through p with slope = -1/7 is y = -x/7+b
1/5 = -1/7 + b so b = 1/5+1/7 = 12/35
The equation of the line is y=-x/7 +12/35

Strange question.

Answer 2

Slope between (1, 1/5) and (x, 1/(5x))
= (1/(5x) - 1/5)/(x-1)
= -1/7
Simplify,
- 1/(5x) = -1/7
x = 7/5
y = 1/7