Question

Do all lines have a y-intercept? Why or why not?

Answer 1

No

Explanation:

I am assuming you are talking about linear functions. When it comes to them, most of them have a y-intercept, and if they do, they are counted as functions. Linear functions must have some sort of slope, but because there is a special line that does not have a slope, then it is not a function. And since it does not have a slope, it also does not hit the y-axis. Usually, the equation is set to equal y, for example:

y = 1

But, a line that does not have a slope is equal to x, like:

x = 1

x = 1 is a completely vertical line that is parallel to the y-axis, which means it does not have a y-intercept.

To experiment this, you can try it in Desmos, which is a secure graphing website. I hope this helps you!

Answer 2

Not all lines have an x- and y-intercept. This line does not cross the x-axis. Similarly, the line x=2 is a vertical line which does not cross the y-axis.

Explanation: