Step-by-step explanation:
Two lines are parallel if they have the same slope and are perpendicular if the product of their slopes is -1
37.a.Parallel slope=¾
b.Perpendicular slope =-1/¾=-4/3
38.a. -2x+5y=9 and 5x+2y=-6
For the first line,5y=2x+9,y=2/5x+9/5
For the second line,2y=-6-5x,y=-3-5/2x
Compare the slopes
2/5 vs -5/2 we see that -5/2 is the negative reciprocal of 2/5 therefore they are perpendicular
39. If both lines are parallel then their slopes are equal. The slope of y=3x-8 is 3
Using the point-slope form, y-y1=m(x-x1)
y--6=3(x--4)
y+6=3(x+4)
y+6=3x+12
y=3x+12-6
y=3x+6
40.The slope of y=¼x-12 is ¼
The negative reciprocal of it is the slope of it's perpendicular that is -1/¼=-4
Using the point slope form, y-y1=m(x-x1)
y-5=-4(x-2)
y-5=-4x+8
y=-4x+8+5
y=-4x+13
