SOLUTION: Find the slope of the line that is perpendicular to 3x+2y=4

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the slope of the line that is perpendicular to 3x+2y=4      Log On


   

Question 114529: Find the slope of the line that is perpendicular to 3x+2y=4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of the line that is perpendicular to 3x%2B2y=4

Perpendicular lines and their slopes: m%5B1%5D+=+-1%2Fm%5B2%5D
In other words, perpendicular slopes are negative+reciprocals+of each other.

3x%2B2y=4….first we need to write this equation in slope_intercept form y+=+mx+%2B+b like this:
2y=+-3x+%2B+4…….divide both sides by 2
2y%2F2+=+-3x%2F2+%2B+4%2F2…….
y+=+-%283%2F2%29x+%2B+2……….this is slope_intercept form, and we see that m%5B1%5D+=-3%2F2 and b=2

m%5B1%5D+=+-3%2F2
Now find m%5B2%5D
m%5B1%5D+=+-1%2Fm%5B2%5D............substitute m%5B1%5D with +-3%2F2
-3%2F2+=+-1%2Fm%5B2%5D………….multiply both sides by +m%5B2%5D+

-%283%2F2%29+m%5B2%5D++=+-%281%2Fm%5B2%5D%29+m%5B2%5D+………….
-%283%2F2%29+m%5B2%5D++=+-1+………….divide bothe sides by +-3%2F2+
-%283%2F2%29+m%5B2%5D%2F+%28-3%2F2%29+++=+%28-1%29%2F%28-3%2F2%29++………….

m%5B2%5D+=+%28-1%29%2F%28-3%2F2%29++………….....we can write -1 as -1%2F1
m%5B2%5D+=+%28-1%2F1%29%2F%28-3%2F2%29++………….simplify
m%5B2%5D+=+%28-2%29%2F-3………….
m%5B2%5D+=+2%2F3…………....your solution