SOLUTION: Why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation?

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this is because the sets of points are a ratio to each other.
the slope of the line is the difference between the two sets of points,
just like 1/2 = 2/4 = 3/6 = 4/8
if on the same line, points (1,1),(2,2) and (15,15) all have a slope of 1 and a y-intercept of 0.