Math And Geometry

Question

Write an equation in slope-intercept form for a line that must contain (-2, -4) perpendicular to a line

Answer 1

an equation in slope intercept form that must contain the point (-2,-4) and is perpendicular to a given line:

if the given line is y=mx+b

any perpendicular line will have a slope that is the negative inverse = -1/m

the equation of the perpendicular line is y=-x/m + a constant term, call it c

y =-x/m +c

plug in the point (-2,-4), x=-2, y=-4

-4 =-(-2)/m + c

-4 = 2/m +c

c = -4 -2/m

y =-x/m -4-2/m

if the original line had slope =2

then the perpendicular line through the given point (-2,-4) is

y =-x/2 -5