Question

Find the x-intercept and the y-intercept for the graph of the equation. 3x y=-3

Answer 1

Let's start with simplifying this equation. Typically we have y = something, so let's rewrite it in this form.

3xy = -3

y = -3/3x

y = -1/x

Alright! Now, let's go ahead and solve for the y-intercept. Those only occur when x=0, so let's plug in 0 for x.

y = -1/0

Slight problem. Dividing by a 0 results in an imaginary number, or "undefined". In this case, there is no y-intercept.

Now we can solve for an x-intercept. These only occur when y=0, so let's set y to 0!

0 = -1/x

Well shoot! We have another problem. No regular number of x will give us a y=0. However, this problem isn't the same as our undefined one from before. Here, as x value approach infinity, we get closer and closer to 0. We can never actually hit 0, but we do approach it. I'm not sure how your teacher wants it answered, but strictly, there is no x-intercept. However, we can actually attempt to explain what is going on, which is that as x go to infinity, we APPROACH y=0.

Hope that helps, and please let me know if you need clarification on anything!