find equation

Question

Find equation of line l where l is perpendicular to y=2/3x. And passes thru point (3,2)

Answer 1

Keri:  In Algebra, there are a couple of things that you need to work this type of problem.  The first is y = mx + b.  The second thing is to know is that m = slope and that the slope of a line perpendicular to another has a slope that is the negative reciprocal of the slope of the first line.  Your first equation is y = (2/3)x.  The slope of the first line is (2/3).  The negative reciprocal of (2/3) is -3/2.  Now plug in the values of the point the second line is passing through, where the y is replaced with the 2 and the x value is replaced with the 3.  Now you have 2 = -(3/2)(3)  + b.  b is going to be the point that the new line will cross on the y axis.  2 = -(9/2)  + b.  When you add the (9/2) to both sides of the equation, you find that b = 2 + (9/2) = (13/2).  Now that you have the b value, again substitute the correct information in the y = mx + b formula to end up with y = -(3/2)x + (13/2).  If you check your answer with a graphing calculator, compare the equations y = (2/3)x and the obtained equation of y = -(3/2)x + (13/2) and you zoom "square," the two lines that show up on the graph will be perpendicular to each other, passing through (3,2).  Good luck!!