+24 convert the equations to standard form if they are not already in it. (y=mx+b)
then compare the slope(m) of each equation. if the two equations have the same slope, they are parallel. if the second slope is the negative reciprocal of the first slope, then the lines are perpendicular. and neither if neither of these are true
Problem A
1st equation Move the 2x over and divide everything by -3 solving for y
y = (2/3)x -4 , 2nd equation y = -2/3 x +5 Not same slope, not negative reciprocal so, Neither
Problem B - again move the x over to the other side, divide by what's in from of the y
1st Equation y = (-3/2) x + 3 2nd Equation y = (+2/3)x - 7/3 Slopes are negative reciprocals therefore perpendicular
Problem C - Easiest one of all - Already in slope intercept form
1st equation slope is 4, 2nd equation slope is (1/4). Tricky, but they're NOT negative reciprocals ( One +, One -) They're only reciprocals so NEITHER
Problem D
1st Equation y = -x +1 Slope is -1 or (-1/1) 2nd Equation y = -1x + 1 Same Slope so should be parallel BUT the y intercept is the same, so its the same line. If your teacher is a *%$% then he could say neither ( a line can't be parallel to itself), or since it is the same slope it is parallel , assuming they are only looking at the slopes. So it has two answers depending on the teachers point of view.
Good luck
+129842 A 2x - 3y = 12 y = -(2/3)x + 5
Solving for y in the first equation, we have, y = (2/3)x - 4........the slope would have to be the same as in the second equation to be parallel and it would have to be the negative reciprocal of the second to be perpendicular......since it's neither, these lines are not parallel or perpendicular
B 3x + 2y = 6 2x - 3y = 7 rearrange both in terms of y
y = -(3/2)x + 3 y = (2/3)x + 7/3 the solpes are negative reciprocals.......these lines are perpendicular
C y = 4x + 13 y = (1/4)x - 13 ......neither
D x + y = 1 2y = -2x + 2 dividing the second equation through by 2, we have y = -x + 1 and adding x to both sides we have x + y = 1 ...........these lines llie on top of each other [ they are the same line ]........so they must have the same slope, but they are not "parallel" in the true sense of the word since parallel lines never intersect
