1.) Do all linear equations have y-intercepts?
All linear equations do not have y-intercepts.
The equation x=10 (which is linear) is simply a vertical line through the x-intercept x=10 but it
does not have a y-intercept since the line is parallel to the y-axis.
2.) Do all linear equations have x-intercepts?
All linear equations do not have x-intercepts.
The equation y=c, where c is a constant is a horizontal line and that does not intercept the x-axis.
3.) Can a linear equation have more than one y-intercept?
One must remember that, a function can only have one output (y-value) for each input (x-value).
A function having more than one y-intercept would violate this, since it would mean that there
are two outputs for x=0. Therefore, it is not possible for a function to have more than one yintercept.
The definition of a linear function prevents the function from having more than one y-intercept.
x-values can't be shared in a function; there is a unique x value for every y value. At the y-axis,
the value of x is 0. two y-intercepts would mean that x would be 0 for TWO points on the linear
function, which doesn't pass the vertical line test and, therefore, isn't a function.
a graph CAN, however, have more than one x-intercept. the line y = 0, which passes the vertical
line test and sits directly on top of the x-axis, has infinitely many x-intercepts and it is still a
linear function.