Show that the lines y=3x+7 and 2y-6x=8 are parallel (not using a graphical method).

The standard form of a straight line is y = mx + c, where y and x are variables that depend on each other, m is the gradient and c is the y-axis intercept. An important fact for this question is that parallel lines have the same gradient.We see the first line is already in the standard form of a line and we can see from inspection that the gradient of y = 3x + 7 is 3.We now seek to get the second line in the same form. By adding 6x to both sides we see that 2y = 6x + 8.Now simply dividing by 2 on both sides we get y = 3x + 4 and we can see that the gradient of this line is also 3Hence the lines are parallel.