Determine if the lines 7x + 3y = 6 and 3x + 7y = 14 are parallel , perpendicular or neither . Solution To establish if 2 lines are perpendicular or parallel, we have to find out the vlues of their slopes. We know the followings about the slopes of 2 lines: - if the 2 slopes have equal values, the lines are parallel; - if the product of the 2 slopes has the value = -1, the lines are perpendicular. So, let\'s find the values of the slopes of the 2 lines. We know that the equation of a line could be written: y=mx+n, where m is the slope of the line. The first line is 7x + 3y = 6. We\'ll subtract 7x and we\'ll obtain: 3y = 6 - 7x We\'ll divide the equality by 3, both sides: y = (-7/3)*x + 6 The slope of the line is m = -7/3 Now, we\'ll find the slope of the second line, 3x + 7y = 14. We\'ll subtract 3x: 7y = 14 - 3x We\'ll divide by 7: y = (-3/7)*x + 14 The slope of the line is m = -3/7 It is obvious that the 2 slopes are not equal, so the lines are not parallel. Let\'s calculate their product: (-7/3)(-3/7) = 1 Because their product is not -1, the lines are not perpendicular..