Show that line 2y − 3x = 4 is parallel to the line 4y = 6x − 1.

Re-arranging 2y − 3x = 4

2y − 3x = 42y = 3x + 4y = 1.5x + 2This line has a gradient of 1.5

Re-arranging 4y = 6x − 1

4y = 6x − 1y = 1.5x − 0.25This line has a gradient of 1.5

As both lines have the same gradient, they must be parallel.

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