For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
If two lines are perpendicular then the product of their slopes is -1, that is:
[tex]m_ {1} * m_ {2} = - 1[/tex]
If we have the following line:
[tex]y = -2x-4[/tex]
Then [tex]m_ {1} = - 2[/tex]
We find[tex]m_ {2}:[/tex]
[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- 2}\\m_ {2} = \frac {1} {2}[/tex]
Thus, a line perpendicular to the given line will be of the form:
[tex]y = \frac {1} {2} x + b[/tex]
ANswer:
[tex]y = \frac {1} {2} x + b[/tex]
