Question 931491
The slope of the line represented by {{{y=-4x-5}}} is {{{M=-4}}} .
The slope of a line perpendicular to a line of slope {{{M}}}} is {{{m=-1/M}}} ,
so the slope of the line you are looking for is
{{{m=-1/((-4))=1/4}}} .
The x-coordinate of the point the line passes through is zero, meaning that the point is on the y-axis.
In other words that point is the y-intercept of the line.
The equation of a line can be written in the slope-intercept form as
{{{y=mx+b}}} when the slope is {{{m}}} and the y-intercept is {{{"( 0 , b )"}}} ,
so the equation you are looking for is
{{{highlight(y=(1/4)x-1)}}}
 
NOTE: For this problem, the point given "happens to be" the y-intercept.
More generally:
A line of slope {{{m}}} , passing through a point {{{P(x[P],y[P])}}}
can be represented by the equation {{{y-y[P]=m(x-x[P])}}} ,
and that is called a point-slope form of the equation.
So, the line you are looking for, passing through (0,-1) can be represented by the equation
{{{y-(-1)=(1/4)(x-0)}}} <---> {{{y+1=(1/4)x}}}
The equation above is one of the infinite number of equations for the line you are looking for.
The more popular, one and only, slope-intercept form is the {{{y=mx+b}}} form that you find when you "solve for y" :
{{{y+1=(1/4)x}}} <---> {{{y=(1/4)x-1}}} .