Which line is perpendicular to y = 2x - 8

a. 4y = - 2x + 2

b. y = 2x - 4

c. 3x + 2y = - 6

d. y = - 2x + 7

Choice A is correct answer.

Step-by-step explanation:

We have to find a equation of line which is perpendicular to y=2x-8.

The slope of perpendicular lines are negative reciprocals of each other.

y=mx+c is standard form of equation of line where m is slope and c is y-intercept.

given equation is:

y=2x-8

Compare above equation with standard form of equation of line, we get

m=2

The slope of perpendicular lines are negative reciprocals of each other.

Hence, m=-1/2

4y=-2x+2

dividing by 4 to both sides of above equation, we get

Choice A is:

4y/4=-2x+2/4

y=-2/4x+2/4

y=-1/2x+1/2

hence, choice A has slope equal to - 1/2.

4y=-2x+2 is equatio of line perpendicular to y=2x-8.

So, choice A is the answer.

A - Perpendicular lines have negative reciprocal slopes. Therefore a perpendicular line to 2x-8 will have a slope of - 1/2. Once solved in slope intercept form, choice A shows a line of slope - 2/4, equivalent to - 1/2