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Because, in order for the equation to cross the x-axis (for example), the y-value must logically be zero. Otherwise the point that you find would not be along the x-axis; e.g if y=1, the point would be above the x-axis, or if y=-2, the point would be below the x-axis, rather than the intercept on the x-axis.

I.e to plot co-ordinates, you always plot x (across), the y (up or down). To find the x intercept, you need to know how much "across" it is, but you don't want it to be "up or down", since then it won't be the intercept. This is why 'y' must be zero.

The argument is the same for plotting y-axis intercepts.

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Q: Why do you replace y or x with zero in equations that you use x and y intercepts?
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