Question

The equation of the like below is y=1/2x-2

Which is the equation of the line that is perpendicular to ab and passes through the point a?

Answer 1

y = -2x + 3

Explanation:

Lines that are parallel have equal slopes but lines that are perpendicular have slopes that are opposite reciprocals. The slope of the given line is
`(1)/(2)` so the slope of all perpendicular lines will be - 2. The new line must pass through the point A(2, -1). Using the formula y = mx + b and replacing y with -1 and m with -2 and x with 2 gives -1 = -2(2) + b. This will simplify to -1 = -4 + b. Adding 4 to both sides gives 3 = b so the equation is y = -2x+3.