Hi,
I need to understand the logic behind the below statement.
If the product of a line’s x and y intercepts is 0, the line definitely passes through the origin.
I believe that it is not true but I know that I am wrong. However, my reason is that a line like x=3 or y=10, have y and x intercepts as 0 respectively and neither of them pass through origin. I am unable to grasp this concept. Please help.
What’s the x and y intercept of x = 3?
y is 0 and x is 3
No, the x-intercept is indeed 3, but I have no idea how you ended up with a y-intercept of 0.
The line x=3 doesnt intersect y at any point.
Yes, and that’s not synonymous to having a y-intercept of 0.
I see. What would be the y intercept in this case. Correct me if I am wrong, inorder to find the x and the y intercept, we find points where y = 0 and x = 0 respectively. So I assumed in this case if we assume x to be 0, there is no y hence y is 0.
There is no y-intercept. As mentioned above, this is not synonymous with saying that the y-intercept is 0 because that suggests that a y-intercept exists when it does not.
Going back to your actual problem now:
You can’t use x = 3 as an example because it doesn’t even satisfy the premise.
To trigger the statement “If the product of a line’s x and y intercepts is 0”, you at least need the x and the y intercepts to exist. In your example x = 3, a y-intercept does not exist, so it doesn’t make sense to talk about the product of the x-intercept and something that doesn’t exist.
Thank you! I finally understand the flaw in my logic. Appreciate your time