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Let's look at the first one:

by plugging x = 0 into the original equation 3x - y = 6, we get 3 (0) - y = 6, which simplifies to -y = 6 and gives y = -6

The easiest thing to do is to just cover up the 3x part with your finger:

ignore the 3x part of the equation 3x - y = 6 by covering it with your finger

So, we get

put the -6 in the y column next to the 0 in the x column, which shows that ( 0 , -6 ) is a point on our graph -- the y-intercept