the example is a graph with an x and y axis
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There are no intercepts because the curve, xy = 4 is asymptotic. When x = 0 (where the y intercept would be) y is infinite, and conversely, when y = 0 x is infinite.
Yes. A straight line for example, such as y = x.
xy + xy = 2xy
The slope intercept formula is y=mx + b in which m is the coefficent by x, x is the slope, and b is the y-intercept which is why it is called y-intercpet or slope-intercept. An example: y=3x + 7. Here your slope is three and y-intercept 7.
If the function is in this form: y = mx + b Then b is the y-intercept. For example if the function is y = 2x + 4 then the y-intercept is 4.