Please help! (will give brainlist!) 37: given the line y=3/4x-2
a: find the parallel slope.
b: find the perpendicular slope.

38: determine if the lines are parallel or perpendicular:
a: -2x+5y=9 and 5x+2y=-6
b: 4y=8x+12 and -12x+6y=24

39: write an equation of a line that passes through (-4,-6) and is parallel to y=3x-8

40: write an equation of a line that passes through (2,5) and is perpendicular to y=1/4x-12

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