To write a equation of a line to the given equation, we first need to determine its . Two lines are perpendicular when their slopes are negative . This means that the product of the slopes of perpendicular lines is
Note that the given equation is written in .
In the above formula we can see that the slope is
By substituting this value for
into our equation, we can solve for the slope of the perpendicular line,
Any perpendicular line to the given equation will have a slope of
Let us now write a partial equation in slope-intercept form for a perpendicular line to the given equation.
By substituting the given point
into this equation for
respectively, we can solve for the
of the perpendicular line.
Now that we have the
intercept, we can write the equation of the perpendicular line to
through the point