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explain why a function has at most one y-intercept
The y-intercept is the value of the function (if it exists) when x = 0.
The function y = -1 has no x-intercept; its graph is a horizontal line with a y-intercept of -1.
The y-intercept is the value of the function when 'x' is zero. That is, it's the point at which the graph of the function intercepts (crosses) the y-axis. The x-intercept is the value of 'x' that makes the value of the function zero. That is, it's the point at which 'y' is zero, and the graph of the function intercepts the x-axis.
The slope of a function is the y-intercept or the change in y, over the change in x.