How do I find the slope of two-variable linear equation? I'm studying level curves from the stewart text. It says that the level curves of the equation f(x,y) =6-3x-2y are a family of lines with slope -3/2. How?

Question

How do I find the slope of two-variable linear equation?  I'm studying level curves from the stewart text.  It says that the level curves of the equation f(x,y) =6-3x-2y are a family of lines with slope -3/2.  How?

amistre64 · Answer

how do we measure slope?

anonymous · Answer

Rise/run?  Derivative?  Tangent line?  :/

amistre64 · Answer

|dw:1428035804311:dw|

amistre64 · Answer

yeah

now what you have is a plane given to you, the 3d version of a line

z = 6 - 3x - 2y

or

3x + 2y +z = 6,   has a normal to the plane defined by the coeeficients

(3,2,1)

does this make sense?

perl · Answer

level curves are defined as f(x,y) = k , therefore
 6 - 3x - 2y  = k

perl · Answer

that is an equation of a line, solve for y

perl · Answer

lines* plural, because k is a parameter

perl · Answer

$$ \Large{
f(x,y) = 6-3x-2y\
	ext{Level curves are defined as } f(x,y) = k 
\ \implies 	ext {by substitution} \ 
 6-3x-2y = k 


}
$$

anonymous · Answer

I see the light now - thanks to both for your perspectives