goes through (2,-1) and perpendicular to 3x-2y=8

Question

i get confused when i get to the part about handling the -2y 

Answer 1

OK, it's like regular algebra but with letters thrown in.

 

3x -2y = 8

3x - 2y - 3x = 8 - 3x

-2y = -3x + 8

-2y/-2 = -3y/-2 + 8/-2

y = (3/2)y - 4

 

Now, perpendicular lines have opposite, reciprocal slopes. Let's use our point and find b.

 

-1 = (-2/3)2 + b

-1 = -4/3 + b

b = 1/3

 

y = (-2/3)x + 1/3

Answer 2

HI, Ryan.

 

Okay so you need a line perpendicular to 3x - 2y = 8

First, let's write it in slope-intercept form (y = mx + b) :

2y = 3x - 8

y = (3/2)x - 4

So now you see that the slope (m) of the line is 3/2.  So now we can find the slope of the new line by taking the negative reciprocal of the slope.  3/2 = -2/3

 

So the line we are finding has the slope -2/3

y = -2/3x + b

Now, substitute point (2,-1) into this equation to find the y-intercept (b).

-1 = -4/3 + b

b = -1 + 4/3 = -3/3 + 4/3 = 1/3

So the equation of your line is:

 

y = -2/3x + 1/3