The equation of the straight line is 3x + 2y = 7.

So, we can first write it the standard form of y = mx + c.

We have 2x = -3x + 7
Or, y = -\(\frac{3}{2}\)x + 3.5

So any line that is perpendicular to it must have a slope of 2/3 as we know the product of the slopes of two perpendicular line is -1.

Now it means the parallel lines must look like this,
y= \(\frac{2}{3}\)x + c
Or, 3y = 2x + 2c
Or, 3y - 2x = 2c

Now this one can also be written as 2x - 3y = - 2c.

Our main focus must be to see if we have the variable part as 3y - 2x or 2x - 3y or y= \(\frac{2}{3}\)x

So when we see lines in these forms we select that.


Only A and F are in this form

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