What is the equation of the line that passes through #(5,7)# and is perpendicular to the line that passes through the following points: #(1,3),(-2,8) #?
First, we will find the slope of the perpendicular line. The slope can be found by using the formula:
Substituting the two points from the problem gives:
A perpendicular line will have a slope (let's call it
Now that we have the slope of the perpendicular line and one point we can use the point-slope formula to find the equation. The point-slope formula states:
Substituting the perpendicular slope we calculated and using the point from the problem gives:
Or, if we solve for