Parallel and Perpendicular Lines

[Guest]

Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.

19. 3y=2x+14
2x-3y=2

20. y=-5x
y=5x-18

21. y=0.6x+7
3y=-5x+30

 

[happy]

Do you know the rules?


The slopes of parallel lines are equal.


The perpendicular slopes are negative reciprocals of each other.

Get them into slope intercept form, first.

If you get stuck, write back showing detailed work.

 

[mad_mathematician]

Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.

19. 3y=2x+14
2x-3y=2

20. y=-5x
y=5x-18

21. y=0.6x+7
3y=-5x+30

19. 3y = 2x + 14
y = 2/3x + 4 2/3 therefore gradient 2/3

2x - 3y = 2
2/3x = y + 2/3 therefore gradient 2/3

Since both these gradients are the same, these lines are parallel

20. no rearranging required, you can tell straight away that the lines are neither parallel (same gradient) or perpendicular (gradients multiply to -1)

I'll leave you to try 21 by yourself, do NOT assume theyll be perpendicular just because that will make one of each