Why do equivalent ratios form a straight line when graphed?

Assume as an example the following equivalent ratio: y1/x1 = y2/x2

If y1 is proportional to x1, then y1 = m*x1 must be fulfilled, where m is some constant. On the other hand, y2 = m*x2 must be fulfilled too; dividing both equations gives y1/y2 = x1/x2 (m is simplified) which can be rearranged as y1/x1 = y2/x2. So, both points (x1, y1) and (x2, y2) belongs to the same line equation, y = m*x

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