Find the points on the graph of y = 1/x where the graph is parallel to the line 4x + 9y = 3.

Answer 1

The slope of the straight line
4x + 9y = 3 is
-9/4.

You want points on the line y = 1/x where
dy/dx = -9/4. Therefore solve
-1/x^2 = -9/4
x^2 = 4/9
x = +2/3 and -2/3.
At those points, y = 3/2 and -3/2, respectively.
Therefore there are two points on the curve that satisfy the slope requirement:
(2/3, 3/2) and (-2/3, -3/2)

Answer 2

Would the slope not be -4/9?