Write an equation for the line perpendicular to y=2x-5 through the point (8,-2)

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

Where:

m: It is the slope of the line

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 equation of the line:

Then

We find

Thus, the perpendicular line will be of the form:

We substitute the given point and find "b":

Finally, the equation is of the form: