urgen math help finding perpendicular lines

Question

Match the following linear equations to the given criteria.

A.         

B.      

C.          

D.             

A line perpendicular to x = 2 

       [ Choose ]         A         B         D         C      

A line parallel to y=2x-7 

       [ Choose ]         A         B         D         C      

A line perpendicular to 2y=3x-10 

       [ Choose ]         A         B         D         C      

A line perpendicular to 2x+3y=18 

Answer 1

A line perpendicular to x = 2 

B  Vertical and horizontal lines are perpendicular

A line parallel to y=2x-7 

The line parallel to this will have the same slope, 2.

-2x+y=4 Add 2x to both sides

 -2x+y+2x=4+2x Simplify

y=2x+4 This has a slope of 2, D    

A line perpendicular to 2y=3x-10  Divide both sides of the equation by 2

2y/2=3x/2-10/2  Simplify

y=3/2 x-5 The line perpendicular to this will have a slope of -2/3 A

A line perpendicular to 2x+3y=18  Subtract 2x from both sides

2x+3y=2x=18-2x Simplify

3y=-2x+18 Divide both sides by 3

3y/3=-2x/3+18/3 Simplify

y=-2/3x+6 The slope of the line perpendicular to this would be 3/2.

3x=2y+1 Switch the equation so y is on the left

2y+1=3x Subtract 1 from both sides

2y+1-1=3x-1 Simplify

2y=3x-1 Divide both sides by 2

2y/2=3x/2-1/2 Simplify

y=3/2x-1/2 C