Line perpendicular

Question

A line contains the points (-1,1) and (5,4)

The slope is 1/2

The equation of the line in point-slope form is: (y-1) = 1/2(x- -1)

The equation of the line in slope-intercept form is: y = (1/2)x + (1/2)

What is the slope of a new line which is perpendicular to the line which is given?

Answer 1

If lines of slope m₁ and m₂ are perpendicular, the slopes satisfy the relation

 

m₁m₂ = -1

 

The line in this problem has slope m₁ = 1/2.  Then any line of slope m₂ = -1/m₁ = -1/(1/2) = -2 is perpendicular.