Hi there--

THE PROBLEM:
Explain in words how to write an equation that is part one: parallel and then also part two: 
perpendicular to the equation y=2/3x-4 passing through the point (-2,-5).

A SOLUTION:
Part I:
To write the equation of a line that is parallel to another line, we use the mathematical idea 
that parallel lines have the same slope. 

Your line  is in slope intercept form (y=mx+b). In this form, the slope of the 
line is the coefficient of the x-term. In other words, the slope is 2/3.

Now we know the slope of the parallel line as well as a point (-2,-5) that the line passes 
through. We can build an equation using the point-slope form for the equation of a line.



In this formula, m is the slope of the line,  and  are the x- and 
y-coordinates of a point on the line. Substituting, we have the equation



This is an equation for the line parallel to the line  through (-2,-5).

If you want, you can simplify the equation by clearing the parentheses and combining like 
terms.


Part II:
To write an equation for a perpendicular line, we use the mathematical idea that when two 
lines are perpendicular, the product of their slopes is -1. (The official mathematical language 
for this is "one slope is the negative reciprocal of the other slope.")

For example, if the slope of one line is 3/4, the slope of the other is -4/3 because


After you find the slope of the perpendicular line, you use the point-slope formula as we did 
above to find the equation of the line.

Hope that helps! Feel free to email me if you have questions about this explanation.

Mrs. Figgy
math.in.the.vortex@gmail.com