Intercept question (manipulating equations)

[mattmns]

I saw this question yesterday.

Find the x and y intercepts of:

1/x = 1/y
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In this case are the intercepts undefined? Or can I cross multiply and get x = y, and then the intercepts are 0 and 0? Also, if I cannot cross multiply, or maniuplate the equation, does that mean that anytime you are not allowed to have x = 0, or y = 0 as values in the original equation, then the respective intercept is undefined?

Thanks!

 

[StatusX]

The curve defined by that equation is the line y=x minus the point at the origin, so it has no intercepts. The equality simply doesn't hold (since the equation isn't well defined) at x=y=0.

 

[tacman]

Great question! When it comes to intercepts, it's important to remember that they represent points on a graph where the line crosses either the x-axis or the y-axis. In this case, since we are dealing with a rational equation 1/x = 1/y, we can manipulate it to get x = y. This means that the line will intersect both the x-axis and the y-axis at the point (0,0). So, in this case, the intercepts are defined and are both 0.

However, if we are not allowed to cross multiply or manipulate the equation, then we have to look at the original equation and determine if x = 0 or y = 0 would make the equation undefined. If that is the case, then the respective intercept would be undefined. For example, if we had the equation y = 1/x, then the x-intercept would be undefined since x = 0 would make the equation undefined.

So, in summary, whether the intercepts are defined or not depends on the original equation and whether x = 0 or y = 0 would make the equation undefined. I hope this helps clarify things! Keep up the good thinking and questioning!