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Which equation represents a line which is parallel to the line y, equals, start fraction, 2, divided by, 3, end fraction, x, minus, 6y= 32​ x−6?

Question

Which equation represents a line which is parallel to the line

y = \frac{2}{3}x - 6y = 32?

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Solution

The equation you provided seems to be a bit mixed up. However, if the equation is y = 2/3x - 6, then any line parallel to this would have the same slope, which is 2/3.

So, the equation of a line parallel to y = 2/3x - 6 could be y = 2/3x - 4, y = 2/3x + 5, y = 2/3x + 1, etc. The "-4", "+5", "+1", etc. are the y-intercepts and can be any real number. The key is that the slope (2/3) remains the same because parallel lines always have the same slope.

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