write down the equation of a line that is perpendicular to y=2x-1 and passing through (4,0)

Answer 1

y=2x-1 has a perpendicular line with slope -1/2, which is the negative inverse of 2, the coefficient of the x term. when a linear equation is solved for y, the slope is the coefficient of the x term. 2 = 2/1. flip that fraction upside down and change its sign to get -1/2 = m, as the slope of the perpendicular line.

y = mx +b where m=-1/2. solve for b by plugging in the point (4,0)

0=(-1/2)(4) + b

b =2= y intercept

the perpendicular line is: y=-x/2 + 2

or y=(-1/2)x +2 in slope intercept form

or x+2y =4 in standard form

or y-0 = (-1/2)(x-4) in point slope form

or x+2y-4 = 0 in general form