parallel pairs,perpendicular pairs equations

Question

Consider the following equation of lines 

y=3x-5 
y=5
6x-2y+5=0
2x+6y+5=0
x-4=0
y=-0.5x+5

without graphing the lines; select pairs of equations of graphs;

a) slope upward to the right (explain)
b) that are parallel (explain)
c) are perpendicular (explain)
d) slope downward to the right (explain) 
 

Answer 1

These are your equations:

 

(1)    y = 3x-5 
(2)    y = 5
(3)    y = 3x+(5/2)  ------>  rewritten
(4)    y = -(1/3)x - (5/2)  --------> rewritten
(5)    x = 4   -------->  rewritten
(6)    y = -0.5x+5

 

a)

 

1 and 3 because they have positive slopes.

 

b)

 

1 and 3 because they have exactly the same slopes.

 

c)

 

3 and 4 because their slopes are negative reciprocals.

 

2 and 5 because one line is vertical while the other is horizontal.  When these two lines meet, they form perpendicular lines.

 

 

d)

 

4 and 6 because these lines have negative slopes.