Are the pairs of lines parallel, perpendicular, or intersecting?
1. y=−2/3x+7
−2x−3y=12
2. y−6=1/4(x+2)
y=−4x−10
3. 2x−y=7
3x−4y=−8
A. Intersecting
B. Perpendicular
C. Parrallel
1. The first equation can be rewritten as y=(-2/3)x+7, which has a slope of -2/3. The second equation can be rewritten as y=(-2/3)x+4, which also has a slope of -2/3. Since the slopes are equal, the lines are parallel.
2. The first equation can be rewritten as y=(1/4)x+8, which has a slope of 1/4. The second equation can be rewritten as y=(-4)x-10, which has a slope of -4. Since the slopes are not equal, the lines are not parallel. To determine if they are perpendicular, we can check if the product of their slopes is -1: (1/4) * (-4) = -1. So, the lines are perpendicular.
3. The first equation can be rewritten as y=2x-7, which has a slope of 2. The second equation can be rewritten as y=(3/4)x+2, which has a slope of 3/4. Since the slopes are not equal, the lines are not parallel. To determine if they intersect, we can solve the system of equations:
2x-y=7 and 3x-4y=-8. Solving this system will give us the point of intersection, if it exists.