Question

Why can't the intercepts, on their own, be used to graph the relation 5x + 9y = 0?

Answer 1

The reason is: Because this line passes through the origin.
In other words, both the x-intercept and the y-intercept are zero.
The two intercepts coincide, so they give you only one point on
the line, and that's not enough information to draw the line.

Answer 2

so the intercepts are when the point is at that axis or when the other axis is zero so set each to zero
if x=0 then y=0
vice verca
doesn't help much
you would need slope to help