Question

Determine whether the graphs of the given equations are perpendicular, parallel, or neither.
y=4x - 2 & -x + 4y=0

Two lines with positive slopes are parallel.
a. always
b. sometimes
c. never

Two lines with the same slope and different y-intercepts are perpendicular.
a. always
b sometimes
c. never

Answer 1

y = 4x - 2
-x + 4y = 0.....4y = x ...y = 1/4x
answer is neither

2 lines with positive slopes are parallel.....SOMETIMES....they would have to have the exact same positive number to be parallel. 

2 lines with same slope and different y int. r perpendicular....NEVER. Lines with same slope and different y int are parallel, not perpendicular

Answer 2

1. The two equation of line are

a. y = 4 x -2

b . -x + 4 y=0→ x=4 y→y =$\frac{1}{4}$

Slope intercept form of line is , y= m x + c

Slope of line a =4

Slope of line b = $\frac{1}{4}$

Neither the product of slopes of two lines is -1, nor their slopes are equal.So, these two lines are neither parallel , nor perpendicular to each other.

Correct option is neither.

2. Two lines with positive slopes are parallel→Incorrect Statement

Two lines with same slope either positive or negative  are parallel.

Correct Option (Sometimes)

3. Two lines with the same slope and different y-intercepts are perpendicular.→→Incorrect Statement(never)

For lines to be perpendicular , the product of their slopes should be -1.

Lines having same slope are always parallel to each other, there is no effect of y intercept.