Are the two lines 2y-x=6 and 2x-4y=(-16) parallel or perpendicular? why?

find the equation of the line that passes through the point (-1,3) that is perpendicular to the line y=-1/2x+7

parallel because they have the same slope

y = 2x + 5

Step-by-step explanation:

The first question is asking whether the two lines are parallel or perpendicular.  Parallel lines have the same slope and perpendicular lines have reciprocal opposite slopes.  To find the slope, you need to convert each of the given equations to slope-intercept form, y = mx + b:

2y - x = 6  or 2y = x + 6 (divide by 2)  y = 1/2x + 3

2x - 4y = -16 or -4y = -2x - 16 (divide by -4) y = 1/2x + 4

Since the lines have the same slope of 1/2, they are parallel.

Given that perpendicular lines have reciprocal opposite slopes, the slope of a line perpendicular to y = -1/2x + 7 would be '2'.  With a slope of 2 and point of (-1, 3):

y = mx + b or 3 = 2(-1) + b

3 = -2 + b

b = 5

y = 2x + 5

a

step-by-step explanation: