Write the equation of a line that is perpendicular to the given line and that passes through the given point. –x + 5y = 14; (–5, –2)

Greetings and Happy Holidays!

1) Perpendicular to 
In order for lines to be perpendicular, their slopes must be negative reciprocals.
Example of slopes with negative reciprocals: 5 and 

First, rearrange the equation into slope y-intercept form:








The slope of the equation is: \frac{1}{5}

The negative reciprocal formula: 

Solve for the negative reciprocal: 


Divide both sides by








The slope of the new line is: -5

2) Passes through (-5,-2)

Create an equation with the slope discovered in slope y-intercept form.


Input the point the line passes through.


Solve for b (the y-intercept).


Multiply.


Add -25 to both sides.




The y-intercept is equal to -27

The Equation of the line is:


I hope this helped!
-Benjamin