Step-by-step explanation:
3)
2x + 3y = 12
Solve for y. Then you have y = mx + b, and m is the slope.
3y = -2x + 12
y = -2/3 x + 12
slope = -2/3
6x - 4y = 8
-4y = -6x + 8
y = -6/(-4) x + 8/(-4)
y = 3/2 x - 2
slope = 3/2
Since the slopes -2/3 and 3/2 are opposite reciprocals, the lines are perpendicular.
4)
3x - 4y = 12
-4y = -3x + 12
y = -3/(-4) x + 12/(-4)
y = 3/4 x - 3
slope = 3/4
4x + 3y = 15
3y = -4x + 15
y = -4/3 x + 5
slope = -4/3
Since the slopes 3/4 and -4/3 are opposite reciprocals, the lines are perpendicular.
