No it is not parallel, here is the reasoning.

First we work out the gradient of the line AB. We do this by using the gradient formula (Y2-Y1)/(X2-X1). Our points are A=(1,3) rewritten as (X1,Y1) and B=(-2,-1) rewritten as (X2,Y2). If we sub in these points into the gradient formula we get: (-1-3)/(-2-1) = (-4/-3) = (4/3)

For two lines to be parallel, the gradients of the two lines must be equal. To find the gradient of the line 3y=4-2x we divide through by the 3 to get y=4/3 - (2/3)x We have then rearranged this line into the form y=mx+c, the standard straight line equation where m = the gradient.

we can see that the m in the equation y=4/3-(2/3)x is (-2/3) which is not the same as 4/3 therefore the gradients of the two lines are not the same and the lines are not parallel.

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