Consider the line y = -7x+6.
find the equation of the line that is parallel to this line and passes through the point (
5
5
)
find the equation of the line that is perpendicular to this line and passes through the point (5,-5).

For this case we have that by definition, the equation of a 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

We have the following equation:

With slope

By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:

We replace the point (5,5) through which the line passes and find "b":

Finally, the equation is:

On the other hand, if two lines are perpendicular then the product of their slopes is -1. Thus, the slope of a perpendicular line will be:

Thus, the equation is of the form:

We substitute the point (5, -5) through which the line passes and find "b":

Finally, the equation is: