For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
By definition, if two lines are perpendicular then the product of their slopes is -1.
We have the following line:
[tex]y = -x + 5[/tex]
The slope is[tex]m_ {1} = - 1[/tex]
We find [tex]m_ {2} = \frac {-1} {m_ {1}} = \frac {-1} {- 1} = 1[/tex]
Thus, the equation of the perpendicular line is of the form:
[tex]y = x + b[/tex]
We substitute the point [tex](x, y) :( 5, -1)[/tex]and find "b":
[tex]-1 = 5 + b\\-1-5 = b\\-6 = b[/tex]
Finally, the equation is:
[tex]y = x-6[/tex]
Answer:
[tex]y = x-6[/tex]
