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You can have infinitely many lines through one specific point, each with a different equation. If you want to have a general equation for ANY line that goes through that point, use the point-slope equation for a line, and use a variable for the slope.
It is convenient for different people to agree on the standard order of operations. This saves complicated explanations.
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A vertical line HAS NO slope! The slope is undefined in this case.
When formatting the equation of a given line into slope-intercept form.