# Thread: X & Y Intercepts

1. ## X & Y Intercepts

Hey everyone, for this one I am suppose to find the x & y intercepts but what do I do if there is no Y intercept..

$\displaystyle x^2y - xy +1 = x$

2. $\displaystyle x^2y - xy +1 = x$

$\displaystyle x^2y - xy = x-1$

$\displaystyle y(x^2 - x) = x-1$

$\displaystyle y = \frac{x-1}{(x^2 - x)}$

$\displaystyle y = \frac{x-1}{x(x - 1)}$

$\displaystyle y = \frac{1}{x}$

3. Well this is just precalculus so would that mean that there is no Y intercept? I'm not sure because the problem states find the X & Y intercepts.

4. You are correct $\displaystyle y = \frac{1}{x}$ has no X or Y intercepts

You can see this by $\displaystyle x,y \neq 0$

5. Originally Posted by pickslides
$\displaystyle x^2y - xy +1 = x$

$\displaystyle x^2y - xy = x-1$

$\displaystyle y(x^2 - x) = x-1$

$\displaystyle y = \frac{x-1}{(x^2 - x)}$

$\displaystyle y = \frac{x-1}{x(x - 1)}$

$\displaystyle y = \frac{1}{x}$ Mr F adds: $\displaystyle {\color{red}x \neq 1}$. The graph of this hyperbola has a hole at (1, 1).